Date: 1. L-R Circuit - RBVRR Womens...

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Department of Physics

R.B.V.R.R.WOMEN’S COLLEGE (AUTONOMOUS) Name:

Roll No:

Date:

1. L-R Circuit

Aim: To study the frequency response of L-R circuit.

Apparatus: A suitable resistance R (or a resistance box of 0-10000Ω) and a correspondingly suitable

inductor L (an air core coil with L = 30mH, r = 50Ω) a sine wave audio frequency generator (signal

generator), Electric Voltmeter(EVM) and connecting wires.(Decade resistances inductance boxes may

be also used)

Formula: By frequency response of an ac circuit we mean how the gain varies with frequency of the

input signal. Frequency response is | ν0/νi| . Here ν0 is the output voltage and νi is the input signal

voltage.

The output may be taken either across the inductor or across

the resistor and we get two frequency response curves. One is

with f on x axis and

[(ν0)L / νin] = (ν0)(across L) / νin on y axis

And the other with f on x axis and [(ν0)R / νin]

= (ν0)(across R) / νin on y axis.

Theory:

The frequency response of any ac circuit implies the variation

of the gain (Voutput/ Vinput) with the input ac signal frequency.

Here, in a LR circuit we can take the output either across from

the resistor or across the inductor. Hence we shall be having two frequency response curves.

Procedure: Take suitable values for R and L and connect the circuit. For a mean frequency f = 1.5 KHz,

νR and [νL = (r2 + (2πL)

2) I] should be nearly equal. Hence, R is to be chosen at a value of 270Ω. The

Audio Frequency oscillator(Signal generator) is set to a conveniently low value at about 5V at a

frequency of 50 Hz. Next measure the output voltage across inductor as VL and across resistor as νR with

the EVM. Now, increase the frequency in convenient and regular steps up to 5KHz and at each step

measure νR and νL with EVM.

Precautions:

1. Connecting wires should be straight and short

2. The ends of the connecting wires should be scrubbed with a sand paper.

3. For each set of readings, νi should also be measured and it should be ensured that νi remains the

same for the whole range of variations in f.

Result:

Lecturer signature with date:

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Viva questions

1. What is r in series with inductor L in the circuit?

2. Why should be that connecting wires short and straight?

3. What is the unit of inductance?

4. On what factors does the inductance depend upon?

5. How do you reduce the self inductance of a resistance coil?

6. What is the phase relationship between ac current and voltage in an inductor?

7. When will be the νL value maximum in this experiment.

8. Why is the current through a pure inductor is called wattles?

9. Why do you use an air-core inductor in this experiment?

10. What is the Q factor of an inductor?

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Observations: Constant voltage ouput from S.G νin = 5 V, R = 270

Frequency f in

Hz

Voltage

across R

νR

Voltage

across L

νL

gain 1(νR/νi) gain 2 (νL/νi)

50 Hz

Calculations and Graph:

Two different graphs are to be drawn. Use semi log graph sheets.

Graph 1:

Log of

frequency in

Hz on x axis

(log f )

Gain (νR / νi)

on y axis

Scale on x axis:

Scale on y axis:

Graph2:

Log of

frequency in

Hz on x axis

(log f )

Gain (νL / νi)

on y axis

Scale on x axis:

Scale on y axis:

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Date:

2. VERIFICATION OF KIRCHHOFF’S LAWS

Aim: To verify Kirchhoff’s laws in electricity.

Apparatus: 6V battery or a battery eliminator, three resistance boxes each of range 0-10,000 Ω, digital

multi meter, plug key and connecting wires.

Formula: In the analysis of any complicated net work, Kirchhoff’s laws are very much useful. They are

(1) the algebraic sum of currents meeting at a junction is zero. That is

Σ I = 0. ---------------1 This is called junction theorem.

Or

The sum of the current flowing towards a junction is equal to the sum of the current flowing out of the

junction. That is Σ I in = Σ I out -----------------1(a)

(2) The algebraic sum of the potential drops in any closed mesh is equal to the algebraic sum of emf s in

the closed circuit. That is Σ I R = Σ E -------------- (2)

Here the emf E is to be taken as positive if the current transverse the seat of emf from negative terminal

to positive terminal. And the potential drop (along the direction of current) is taken as positive.

Let us consider the circuit shown above

At the junction B, we have from Kirchhoff’s first law i1 = i2+i3 ------- (3)

From Kirchhoff’s second law, we have

(1) for the closed mesh (1) => ABEFA

i1R1 +i3R3 = E -------- (4)

(i.e.) V1 + V3 = E -------- (4) a

(2) For the closed mesh (2) => BCDEB i2R2 – i3R3 = 0 -------- (5)

As we have taken i2 as positive, i3 will be negative

(ii) V2-V3=0 or V2=V3 --------5(a)

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(3)For the closed mesh ACDFA

i1R1+i2R2 = E ------- (6)

(ii) V1+V2 = E ------ 6(a)

In our experiment we shall prove equations 3,4a, 5a and 6a to verify Kirchhoff’s laws.

Description:

We have to use a 6V battery or a battery eliminator. The resistances should be of non-inductive type. We

can use the digital multi meter for convenience sake.

Theory: Kirchhoff’s laws are universal and can be applied to any kind of network. They are applicable

for a.c. circuits also, with the only difference that in the case of ac we have to use complex quantities for

voltages, current and impedances.

Kirchhoff’s first law is a consequence of conservation of charge and the second law is a consequence of

conservation of energy.

Kirchhoff’s laws can be stated in different forms with different sign conventions. But, we are here

following the simplest and straight form.

Procedure:

Circuit connections are made as shown in figure. This network is called a T network as it is T shaped at

B. the emf of battery is measured with EVM as E. Initially 1000Ω resistances are used each in R1 and

R2. The plug key (K) is closed. Resistance in R3 is first kept at 1000Ω and the potential differences V1

across R1, V2 across R2 and V3 across R3 are measured with EVM or digital multi meter. Next, the

resistances in R3 is gradually increased in steps of 1000Ω each time up to 10,000 Ω and at each step V1,

V2 and V3 are measured. The corresponding currents are given by i1=V1/F1, i2=V2/R2 and i3=V3/R3. The

values are tabulated in table-1.

The experiment may be repeated with different combinations of R1 and R2

Precautions:

1. The connections should be made carefully having no loose contacts.

2. The resistances should be of non-inductive type.

3. The connecting wire ends should be scrubbed with sand paper.

4. In case of resistance boxes, expect the unplugged ones, all the remaining keys should be closed

very tight.

5. The connecting wires should be short in length and straight.

Result:


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Observations:

Table-1

R1 = 1000Ω, R2 = 1000Ω

S.No Resistance Potential difference Current in amps

R3(Ω) V1 (V) V2(V) V3(V) i1=V1/R1

(A)

i2=V2/R2

(A)

i3=V3/R3

(A)

Calculations: For verification of Kirchhoff’s laws, the readings in table-1 are transferred in table-2

EMF of the battery V = V

S.No i1 (A) (i2 + i3)

(A)

V1+V3 (V) V1+V2 (V) V2(V) V3 (V)

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Possible viva questions

1. Are there any other forms of Kirchhoff’s laws.

2. What sign conventions are followed in this experiment?

3. What conservation laws do Kirchhoff’s laws represent?

4. What other names are given to Kirchhoff’s laws?

5. Are Kirchhoff’s laws applicable in ac circuits?

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Date: 3. LCR Series Resonant Circuit

Aim : To study the frequency response of a LCR series circuit, and determine its bandwidth & Quality

factor.

Apparatus: Inductors, Resistors, Capacitors, Signal generator, meter for measurement of deflection and

connecting wires.

Theory : A series LCR circuit is said to be in resonance when the current in the circuit is in phase with

the applied voltage or when the impedance of the circuit is minimum at resonance.

This happens when the reactance offered by the inductor in the circuit is equal to the reactance offered

by the capacitance in the circuit. i.e.,

The resonant frequency

At resonance,

1. The impedance Z = R is minimum and purely resistive.

2. The current is maximum. Hence the circuit is known as an acceptor circuit.

3. Voltage magnification ‘m’ is equal to quality factor Q.

Definition of quality factor: The quality factor is the measure of the efficiency of the circuit to store

energy in an inductor or capacitor , when an alternating current is applied.

It is defined as 2π times the ratio of the energy stored to the average energy lost per period.

4. Band width is defined as the group of frequencies with a response of 70.7% of the maximum

response.

f1 and f2 are called half-power frequencies(points) because the power drops to half its

maximum value at these frequencies. Since we are measuring voltage (or current) in the circuit to study

the frequency response, half power points are located by finding where the voltage (or current) drops to

1 / 2 (or 0.707) times its maximum value.

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Circuit diagram:

Circuit diagram for deflection meter

Internal connection in the board to the meter

(need not be connected)

Procedure :

Connect the circuit as shown. Select one combination of LCR and a particular frequency range. Adjust

the amplitude knob in the function generator to give a small deflection in the meter . Now slowly

increase the frequency of the signal till you see a slow increase in the deflection. This deflection reaches

a maximum at a particular value of frequency. See that this maximum deflection does not go beyond the

scale of the meter. This can be done by adjusting the amplitude knob on the signal generator. If the

frequency of the signal generator is further increased, the deflection in the meter decreases and attains

minimum. This variation of the deflection with frequency, that is increasing with deflection becoming

maximum and then decreasing gives the frequency response and also the resonance curve.

The frequency at which the maximum deflection occurs is called the resonance frequency of that

combination(L-C-R).

Repeat the above procedure by changing ‘C’ in the circuit and also by changing ‘R’.

For sharp increase in current at resonance the series resistance should be small which implies that the

resistance of the signal generator should be small.

(a)Effect of capacitance on resonant frequency:

Without changing the inductor and resistance in the circuit the frequency response is studied for

different values of capacitance. Note the observations in table1(a).

The deflection is made maximum by adjusting the amplitude for every ‘C’ value. The output is

measured across ‘C’.

It is observed that resonant frequency fr depends on C.

(b)Effect of resistance on resonant frequency:

Without changing the capacitor and inductor in the circuit the frequency response is studied for

different values of R. Note the observations in table(b).

The deflection is made maximum for the smallest value of resistance, and the output taken across ‘C’ for

all the three resistance value without changing the settings in the signal generator.

It is observed that for small values of R, resonant frequency is independent of R. But Q factor is

inversely proportional to R.

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Graph: A graph is drawn between frequency on X-axis and Deflection proportional to voltage on

Y-axis, for observing the effect of capacitance and effect of resistance.

From effect of resistance graph:

Note down the maximum value of deflection for one curve. Then find 70.7% of the maximum

value V0= 70.7% Vm. Mark this value on the Y-axis. Then draw a line parallel to X-axis from this point.

The line cuts the curve at two points, drop perpendiculars from these two points on to the X-axis . Let

them cut at f1 and f2. Then

f2-f1 gives the band width and the frequency at the maximum value Vm gives fr. Then Quality factor is

Repeat the same for other two curves.

Precautions:

1. Reading should be taken on either side of the resonance frequency fr. For this the values of ‘f’ lower

than fr and the values of ‘f’ higher than fr should be symmetrically distributed around fr on either side.

2. Reading should be taken with out any parallax error.

Note: 1. While taking observations changing the capacitance in the circuit adjust the amplitude in the function

generator so that the deflection in the meter is maximum at resonance for each capacitor.

2. On the other hand while changing the resistance in the circuit adjust the amplitude in the function

generator so that the deflection in the meter is maximum for the smallest resistance at resonance. With

the same settings change the resistance value and take the observations.

3. The deflection in the D.C micro ammeter on the board is proportional to the A.C voltage applied to it.

4. The D.C micro ammeter is converted into a D.C voltmeter by connecting a series high resistance and

a bridge rectifier is used to convert A.C to D.C.

Result:

Lecturer Signature with date:

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Roll No:

Observations and Tables :

Table I(a) :

Deflection across ‘C’ proportional to Voltage varying ‘C’ keeping L and R constant.

C1 = F C2 = F C3 = F

L = mh R =

S.No Frequency in (Hz) with capacitors Deflection in the meter for output across

C1 C2 C3 C1 C2 C3

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Table I(b) :

Deflection proportional to voltage across ‘C’ varying ‘R’ keeping L and C constant.

L = mh C = F

R1 = R2 = R3 =

S.No Frequency in( Hz ) with Resistance Deflection across C for Resistance

R1 R2 R3 R1 R2 R3

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Table II: Calculate of Q:

S.No

Capacitance

C F

Inductance

L mh

Resistance

R Ohms

Resonant frequency Hz Band

Width (f2 -f1)

Hz

Quality

factor

Q =

fr / (f2 – f1)

Observed

from

graph

Theoretical

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Roll No:

Date: 4. LCR Parallel Resonant Circuit

Aim : To study the frequency response of a LCR parallel circuit and determine its band width & Quality

factor.

Apparatus : signal generator, resistors, capacitors, inductors, meter for measurement of deflection and

Connecting wires.

Theory : A LCR parallel circuit is said to be in resonance when the current in the circuit is in phase

with the applied voltage or when the impedance of the circuit is maximum at resonance or when

admittance of the circuit is minimum at resonance.

Theoretically this happens when

This happens when ωC =ω L/R²+ωrL²

C = L/R²+ωrL²

The resonant frequency fr = ωr/2π = 1 √(1 - R²)

2 (LC L²) At resonance,

1. The impedance Z = R² + ωr L² = L/CR is maximum

R

2. The line currenting is minimum. Hence the circuit is known as a rejecter circuit.

3. Current magnification m is equal to quality factor Q

m = ωrL/R = 1/ωrCR = Q = fr/ f2 – f1

4. The band width f = f2 – f1 is found by noting the frequencies corresponding to

1/ √2 or 0.707 times the maximum value of voltage across the capacitor branch.

At resonance the line current ‘io becomes minimum. The branch current ‘i’ flows through the arms of

the tank circuit giving raise to oscillations. Due to this there is a conversion of energy from magnetic

energy to electrical energy and vice versa.

At resonance the voltage across the branch or branch current in the tank circuit increases with

increase in applied frequency, reaches a maximum and then decreases, where as the line current

decreases with increase in applied frequency, reaches a minimum and then increases. These two

variations give the frequency response of the LCR-parallel circuit.

Circuit Diagram :

Circuit diagram for deflection meter

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Procedure :

Connect the circuit as shown in fig(1). Select one combination of LCR and a particular frequency

range. Adjust the amplitude knob in the function generator to give a small deflection in the meter . Now

slowly increase the frequency of the signal till you see a slow increase in the deflection. This deflection

reaches a maximum at a particular value of frequency. See that this maximum deflection does not go

beyond the scale of the meter. This can be done by adjusting the amplitude knob on the signal generator.

If the frequency of the signal generator is further increased, the deflection in the meter decreases and

attains minimum. This variation of the deflection with frequency that is increasing with deflection

becoming maximum and then decreasing gives the frequency response and also the resonance curve.

The frequency at which the maximum deflection occurs is called the resonance frequency of that

combination(L-C-R).

Repeat the above procedure by changing ‘C’ in the circuit and also by changing ‘R’.

For sharp increase in current at resonance the series resistance should be small which implies that the

resistance of the signal generator should be small.

Note:

1.Since the impedance of a LCR parallel circuit is high at resonance the signal generator should have

matching high input impedance.

2. The output is taken across the tank circuit always. (Across the terminals of the capacitors).

3. RO is the resistance in series with the signal generator to limit the line current.

(a)Effect of capacitance (or inductance) on resonant frequency.

Without changing the inductor and resistance in the circuit the frequency response is studied for

different values of capacitance. Experiment may be repeated for different values of inductance.

It is observed that resonant frequency fr and quality factor Q depend on L and C.

(b)Effect of resistance on resonant frequency.

Without changing the capacitor and inductor in the circuit the frequency response is studied for

different values of R.

It is observed that for small values of R resonant frequency is independent of R. But Q factor is

inversely proportional to R.

Graph: A graph is drawn between frequency on X-axis and Deflection proportional to voltage on Y-

axis, for observing the effect of capacitance and effect of resistance.

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Note: 1. While taking observations changing the capacitance in the circuit adjust the amplitude in the

function generator so that the deflection in the meter is maximum at resonance for each capacitor.

2. On the other hand while changing the resistance in the circuit adjust the amplitude in the function

generator so that the deflection in the meter is maximum for the smallest resistance at resonance. With

the same settings change the resistance value and take the observations.

Precautions: 1. Reading should be taken on either side of the resonance frequency fr. For this the values of ‘f’ lower

than fr and the values of f higher than fr should be symmetrically distributed around fr on either side.

2. Reading should be taken with out any parallax error.

Result:


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Observations and Tables :

Table I(a) :

Deflection across ‘C’ proportional to Voltage varying ‘C’ keeping L and R constant.

C1 = F C2 = F C3 = F

L = mh R =

S.No Frequency in (Hz) with capacitors Deflection in the meter for output across

C1 C2 C3 C1 C2 C3

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Table I(b) :

Deflection proportional to voltage across ‘C’ varying ‘R’ keeping L and C constant.

L = mh C = F

R1 = R2 = R3 =

S.No Frequency in(Hz ) with Resistance Deflection across C1 for Resistance

R1 R2 R3 R1 R2 R3

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Table II: Calculate of Q:

S.No

Capacitance

C F

Inductance

L mh

Resistance

R Ohms

Resonant frequency Hz Band

Width (f2 -f1)

Hz

Quality

factor

Q =

fr / (f2 – f1)

Observed

from

graph

Theoretical

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Possible viva Questions(LCR series and parallel)

1.What do you mean by electrical resonance in this experiment?

2.What is the difference in the type of resonance in a series LCR circuit and a parallel LCR circuit?

3.Define quality factor?

4.What happens to the resonance curve and the value of Q as the resistance increases?

5.At resonance what happens to the impedance in a series LCR circuit?

6.How will be the current and voltage across the resistor in an A.C circuit?

7.Why is a LCR series circuit called an acceptor circuit?

8.What are the applications of resonance circuit?

9.What happens to the impedance at resonance in a parallel LCR resonance circuit?

10. Why a parallel resonance circuit is called a rejector circuit?

11.What is the relation ship between the Q factor and band width?

12.What is the essential difference between series and parallel resonant circuit?

13.Is there any difference between series and parallel resonance conditions?

14. What is the power factor in series LCR circuit at resonance?

15.How will be the power delivered to the circuit by the applied source at resonance?

16.What is admittance and what are its units?

17.What is the reactance offered by the capacitance and inductance in the LCR circuit?

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Date:

5. Power factor of an inductive circuit

Aim: To determine the Power factor of an inductive circuit (LR Circuit).

Apparatus: Inductance, three A.C voltmeters or a multimeter, a non- inductive resistance box, a step

down transformer and connecting wires.

Principle: In the following circuit L and R are in series. Therefore the current through both is same. If

the current direction is represented by the base line of the vector diagram shown, the voltage across the

inductance can be represented by the vector VL making an angle ‘θ’ with the base line.

The voltage across resistance is in phase with the current. Therefore it can be represented by a

vector VR which coincides with the direction of the current.

The effective voltage across the entire circuit can be represented by a vector V which is equal to

the vector sum of VR and VL, which makes an angle Φ with the base line. Then CosΦ is called the power

factor of the circuit.

Phasor diagram:

Vector diagram of voltage :

Cos Ф = VR = VR

V √ VR 2+ VL

2

Theory : In an A.C circuit consisting of an inductance L and resistance R, current lags behind the

voltage by a phase angle Ф .

At any instant if V = Vo sin ωt is the applied voltage, then the current in the circuit is

I= Io sin (ωt-Ф) Power P = VI = IoVo sin(ωt-Ф) sin ωt

Average power P = 1/T ∫VoIo sin ωt sin (ωt-Ф) dt

= VoIo cos Ф ∫sin 2 ωt/T dt - (VoIo sin Ф )/ 2 sin 2 ωt/T dt

= (VoIo cos Ф)/2 (average value of sin2t for one cycle = ½ and

Average value of sin 2t for one cycle = 0)

= Vo/2. Io/2 cos Ф

= Vrms Irms cos Ф

P = apparent power. Cos Ф [V rms I rms = apparent power ] Cos Ф --- power factor

P --- true power which is measured by a watt meter

Vrms.Irms --- apparent power, which is obtained by measuring V& I using A.C voltmeter, and A.C.

ammeter.

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True power = apparent power. Power factor

Cos Ф = R/√(R²+(Lω)²) = R/Z

Z --- impedance of the LR circuit

L ω --- inductive reactance

ω --- 2πf

Effect of R on cos Ф

Cos Ф = R/R√(1+(Lω/R)²) = 1/√(1+(Lω/R)²

Hence as R increases power factor also increases.

Effect of frequency ‘f’ on cos Ф :

Cos Ф = R/ √(R²+(Lω)² = R/√(R²+(2πfL)² Hence as f increases Cos Ф decreases.

Circuit Diagram:

Procedure : Connect the A.C. supply to a circuit containing a non-inductive resistance box ‘R’ in series

with an inductive coil ‘L’. Connect three voltmeters in order to measure the total input voltage V, the

voltage VR across the resistance ‘R’ and the voltage VL across the inductance ‘L’. Keeping suitable

resistance ‘R’ in the box switch on the circuit and note the readings V,VR and VL volts in the three

voltmeters. Now repeat the experiment for different A.C frequencies for one particular L and R and

tabulate results as follows. Also measure the resistance RL of the inductance. After calculating Cos

both cases observe the effect of R and frequency on Cos and write in the result.

Precautions:

1. If the amplitude of the output voltage from the signal generator changes during the experiment, it

should be adjusted.

2. The frequency f( = 2πf) of the oscillator should remain the same through out the experiment.

3. Resistance ‘R’ should be non-inductive.

Result:


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Observations :

Part – I: : (Using a step – down transformer)

Inductance L = mh RL = Ohms Frequency = 50 Hz.

Varying the resistance in the circuit:

R

V

volts

VR

volts

VL

volts

I=VR/

R

amps

Z= V/I = (V.R)/VR

Cos Ф= (R+RL)/Z Apparent

power

VI watts

True

power

VI Cos Ф

watts

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Part – II: ( Using a function generator)

Inductance L = mh RL = Ohms Resistance from box = Ohms

Varying the frequency of A.C supply:

Frequency

Hz

V

volts

VR

volts

VL

volts

I=VR/

R

Z= V/I

=(V.R)/VR

Cos Ф=

(R+RL)/Z

Apparent

power

VI watts

True

power

VI Cos Ф

watts

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Possible viva Questions

1. What is the power factor?

2. What is the power factor for a dc circuit?

3. What is the power factor for a pure inductor?

4. How the voltage and current differ in phase in an inductor?

5. What is a wattles current?

6. Where is the wattles current used?

7. What is the phase difference for ac flow between V and I in a resistor?

8. What is the average value of V or I over a full cycle in a.c?

9. Then, how does a.c. voltmeter and ammeter work?

10. When will be VL and V equal?

11. What are the advantages of an electronic voltmeter?

12. Does the power factor change with frequency?

13. How does the quality factor Q and power factor cos differ?

14. What is alternating current?

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Date:

6. RC Circuit

Aim : To draw the charge and discharge curves of a R.C circuit and find its time constant.

Appararus: Power supply, resistor, capacitor, voltmeter, micro ammeter, bell switch(charge and

discharge key) and connecting wires.

Charging the capacitor through a resistance :

Theory : When a capacitor and resistance are connected in series with a direct current (D.C) source the

voltage across the capacitor Vc takes some time to grow to its equilibrium value Vo. The current I

through the circuit and the voltage across the resistance VR decreases with time and reach zero value

when the capacitor is fully charged.

Vc = Vo (1-e –t/RC

) and Current in the circuit I = Io e–t/RC

When t = RC Vc = Vo (1-e-1

) and Current in the circuit I = Io e-1

= 0.632 Vo = 0.368 Io

The time T = (CR) at which the voltage across the capacitor reaches 0.632 or (1/ e )of its equilibrium

value is called the time constant of the circuit.

Method : Select convenient values of R and C and connect the circuit as shown in the figure. Now press

the bell switch. The ammeter indicates maximum current and the voltmeter across the capacitor reaches

zero. These values are for zero time. Release the bell switch and start the stop clock simultaneously.

Note the current I with time till it reaches zero or minimum value. [take the headings at an a interval of

15 sec]

Repeat the same for measuring voltage VC and VR with time.

Current in the circuit I

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Discharging the capacitor through a resistance:

Theory: When the D.C source is disconnected from the R.C circuit after the capacitor is fully charged

the voltage across the capacitor Vc takes some time to reach zero value. But the current in the circuit

shoots to a maximum value and then decreases with time to zero value.

Vc = Vo e-t/RC

I = Io e-t/RC

When t = RC Vc = Vo e-1

I = Io e-1

= 0.632 Vo = 0.368 Io

Time constant T(=RC) may be defined as the time taken by the current or voltage to fall from the

maximum value to 1/e or 0.368 of its maximum value.

METHOD: Using the same values of R and C connect the circuit as shown in the fig. and allow the

capacitor to be fully charged. Now disconnect the voltage source and short circuit the points A and B

(i.e. disconnect the wire from the positive terminal of the voltage source and connect it to the negative

terminal). Start the stop clock simultaneously and note the values of Vc with time till it reaches almost

zero value. Repeat the process for current I.

Voltage across the capacitor Vc

Current in the circuit I:

Precautions: 1. Connecting wires should be straight and short

2. The ends of the connecting wires should be scrubbed with a sand paper.

Result:


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Observations :

R = Ohms C = F time constant T =RC = sec.

S.No. Time (Sec) Vc volts I μA VR = RI

volts Vc + VR

Note that (VR + Vc) is a constant.

Observations:

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R = C = μf time constant T =RC = sec.

S.No. Time (sec) Vc volts I μA VR = RI volts Vc - VR

Note that Vc – VR is nearly zero.

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Date:

7. MULTIMETER

Aim : To construct and calibrate a D.C voltmeter , D.C ammeter .

Apparatus : Connecting wires , resistances , standard voltmeter , ammeter and DC power supply.

Theory: D.C voltmeter :

Aim : To convert the meter into a voltmeter ,a high series resistance has to be connected to

galvanometer (i.e., micro-ammeter)

Circuit Diagram:

Calculation of the resistance R

Let ‘v ‘ be the voltage to be measured: The meter here can measure a maximum current of 100A

Then using the relation V = I R i.e. I = V / R 100 X 10

-6 = v/(R+1800)

where 1800 is internal resistance of galvanometer or meter to be calibrated

R + 1800 = V / 100 X 10-6

For R = V / 100 X 10-6

- 1800 Ω

a)For voltage range 0-1 v

v = 1V, R = 1 X 10+4

– 1800 = 8200Ω = 8.2 k Ω

The resistance to be connected in series with micro ammeter to convert it into voltmeter

of range 0-1v is 8.2 kΩ

b) For 0 – 10v range

v = 10V , then R = [10 X 104] – 1800

= 98200 Ω = 98.2 kΩ

as 8.2 kΩ is already included the remaining resistance i.e., 98.2kΩ – 8.2kΩ = 90 kΩ

has to be included in the circuit.

90 kΩ = 8.2 kΩ + 82 kΩ

c) For 0 – 100v range

V = 100V

R = 100 X 104 – 1800

= 998200 Ω = 998.2 k Ω

As already 98.2 kΩ is included . so ,900 kΩ is to be added which can be split up as

82 kΩ + 820 kΩ

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Procedure: 1. Connect the circuit as shown in the fig(1)

2. Choose 8.2kΩ resistance for 0-1V range

1. Increase the voltage with the help of potentiometer and note the corresponding meter reading.

2. Repeat it for 10V and 100V range.

Theory: D.C AMMETER: To convert the meter into an ammeter a low shunt resistance has to be

connected parallel.

From the fig potential difference across the galvanometer = potential difference across the shunt

resistance

Where G is the internal resistance of the galvanometer

G ig =S is

1800X10-4

= S [i-10-4

]

S =1800X10-4

/ [ i-10-4

]

For i>>10 -4

amp a shunt resistance has to used.

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a) for 0 - 1 mA

I =1X10-3

A

S = 0.18 /10-3

-10 -4

=0.18 / 0.0009

=200Ω

b) for 0-10mA

I = 10-2

A

S = 0.18 / [10-2

-10-4

]

= 0.18 / 0.00999

=18.2 Ω = 18Ω

c).For 0-100 mA

S = 0.18 / [10-1

-10-4

]

=0.18/0.999

=1.8Ω

Circuit Diagram:

For Calibration of Ammeter

Fig(3)

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Roll No:

Procedure:

1. Connect the circuit as shown in the fig(3)

2. Choose 200Ω resistance for 0-1V range

3. Increase the voltage with the help of potentiometer and note the corresponding meter reading.

4. Repeat it for 10V and 100V range.

Graph: Draw a graph for D.C Voltmeter and D.C ammeter with standard meter reading on the X-axis

and the calibrated meter reading on the Y-axis. Draw all the three graphs on the same sheet.

D.C Voltmeter:

D.C Ammeter:

Precautions:1. Choose proper resistances while doing the connections.

2. The voltmeter should be connected in parallel with the part of the circuit across which

we want to measure the potential difference.

3. The ammeter should be connected in series with the circuit.

Result:


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Observations: D.C Voltmeter:

0-1 V, R = 8.2KΩ 0-10V, R = 98.2kΩ 0-100 V, R = 998.2 kΩ

Standard

Meter

reading

(Volts)

Calibrated

Meter

reading

divisions

Standard

Meter

reading

(Volts)

Calibrated

Meter

reading

divisions

Standard

Meter

reading

(Volts)

Calibrated

Meter

reading

divisions

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Roll No:

Observations: D.C Ammeter

0-1 mA , R = 200Ω 0-10 mA, R = 18Ω 0-100 mA, R = 1.8Ω

Standard

Meter

reading

(mA)

Calibrated

Meter

reading

divisions

Standard

Meter

reading

(mA)

Calibrated

Meter

reading

divisions

Standard

Meter

reading

(mA)

Calibrated

Meter

reading

divisions

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Possible viva questions

1. Why a voltmeter is connected in parallel across to points to measure the potential difference between

them.

2. What is the resistance of an ideal voltmeter . why?

3. How do you increase the range of a voltmeter?

4. How do you know the value of given resistance.

5. What is the use of potentio meter.

6. What is the relation between the ohm and kilo ohm.

7. Why an ammeter is connected in series in the circuit?

8. What is the resistance of an ideal ammeter. Why?

9. What is a shunt?

10. What are the uses of shunt?

Date: 1. L-R Circuit - RBVRR Womens...

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