Ee204 01 DC Review

EE 204 Basic Electronics and Electrical Power

Chapter 1: DC Review

EE 204 Chapter 1: DC Review 1

Some Useful Analogies

• E(V) Voltage ~ Pressure Æ causes ‘something’ to flow • I(A) Current ~ ‘something’ Æ water, charge, flux • R(Ω) Resistance ~ ‘restriction’ Æ prevents the flow


Resistor in Direct Current (DC) Circuits

• Ohm’s Law:

• Voltage in Volts (V) • Current in Amperes (A) • Resistance in Ohms (Ω)

• Will see “E” used instead of “V” when referring to the voltage

of a source (e.g. battery)


V I RVoltage Current Resistance u

u

Resistors in Parallel


1 1 1

1

1

6 16

E I RV II A

u

u :

1 2 2

2

2

6 32

E I RV II A

u

u :

Resistors in Series


1 1 2

1

6 1 31.5

E I R I RV I II A

u u

u : u :

Kirchhoff’s Voltage Law

• The total sum of the voltage rises and drops around a closed loop must be zero:

• In a passive component like a resistor (a sink for the energy), the voltage is higher on the input end (current), and lower” on the output

• For a source of energy like a battery however, the current flows out of the positive terminal and back into the negative terminal


0V ¦

Example 1

• What is the voltage across Resistor R5?


Example 1 Solution

• Consider two loop currents I2 and I3:

• Using KVL on the middle loop:


I1 I2 I3

2 2 5 2 3 1

2 2 3

2 3

0

6 2 12 0

8 2 12 0 Eq.1

R I R I I E

I I I V

I I V

: :

: : m

Example 1 Solution (cont.)

• Using KVL on the right loop:


I1 I2 I3

3 3 6 3 2 5 3 2

3 3 3 2

2 3

0

3 3 4 2 0

2 8 4 0 Eq.2

R I R I E R I I

I I V I I

I I V

: : :

: : m


• Determine I3:


2 3

2 3

3

3

3

8 2 12 0

8 32 16 0

30 4 0

30 40.133

I I V

I I V

I V

I VI A

: :

: :

:

:

Using Eq.1Using Eq.2×4Eq.1 + Eq.2 4

m

m

m u


• Determine I2:

• Determine VR5:


2 3

2

2

2

8 2 12 0

8 2 0.133 12 0

8 11.7341.466

I I V

I A V

I VI A

: :

: :

:

5

5

5

5 2 3

2 1.466 0.133

3.2 positive voltageon top

R

R

R

V R I I

V A A

V V

:

Thévenin’s Theorem

• Any linear electrical network with voltage and current sources and only resistances can be replaced at terminals A-B by an equivalent voltage source Vth in series with an equivalent resistance Rth


Thévenin’s Theorem (cont.)

• The equivalent voltage Vth is the voltage obtained at terminals A-B of the network with terminals A-B open circuited

• The equivalent resistance Rth is the resistance obtained at terminals A-B of the network will all its independent current sources open circuited and all its independent voltage sources short circuited


Example 2

• Determine the voltage across Resistor R5 using Thévenin’s Theorem


Example 2 Solution


3 62 1 2

2 3 6

3 34 12 46 3 3

8

th ab

th

th

R RV V E E ER R R

V V V V

V V

§ · ¨ ¸ © ¹

: :§ · ¨ ¸: : :© ¹

Example 2 Solution (Cont.)


2 3 62 3 6

2 3 6

6 3 33

6 3 3

th

th

R R RR R R R

R R R

R

: : : :

: : :



5

5

5

5

5

2 83 2


R thth

R

R

RV VR R

V V

V V

u

: u

: :

Norton’s Theorem

• Any linear electrical network with voltage and current sources and only resistances can be replaced at terminals A-B by an equivalent current source Ino in parallel with an equivalent resistance Rno


Norton’s Theorem (cont.)

• The equivalent current Ino is the current obtained at terminals A-B of the network with terminals A-B short circuited

• The equivalent resistance Rno is the resistance obtained at terminals A-B of the network will all its independent current sources open circuited and all its independent voltage sources short circuited (note that this is the same as calculating the Thévenin equivalent resistance)


Example 3

• Determine the voltage across Resistor R5 using Norton’s Theorem


Example 3 Solution


1 2

2 3 6

12 46 3 32.667

no ab

no

no

E EI IR R R

V VI

I A

: : :



2 3 62 3 6

2 3 6

6 3 33

6 3 3

no

no

R R RR R R R

R R R

R

: : : :

: : :



5

5

5

5

5 5

55

3 2.667 23 2


R

noR no

no

R

R

V I R

RV I RR R

V A

V V

u

§ · u u¨ ¸© ¹§ ·:

u u :¨ ¸: :© ¹

Power Dissipated in a Resistor

• The power (P) dissipated in a resistor is given by:

𝑃 = 𝑉 × 𝐼

• Making use of Ohm’s law (𝑉 = 𝐼 × 𝑅):

𝑃 = 𝐼 𝑅

𝑃 =𝑉𝑅


KVL Review:

• What is the voltage across R2? • 3V 4V 6V 20V

• What is the current through R3? • 1.2A 10A .30A 3.33A


KCL Review

• What is the current through R2? • .5A 1A 2A 2.5A

• What is the total current coming from the source, E? • .5A 1.5A 2.5A 3.5A

• What is the voltage across R3? • 2V 10V 12V 5V


Thévenin Review

• What is the Thévenin Voltage? • 3.33V 6.67V 10V 20V

• What is the Thévenin resistance? • 6.67 Ohms 10 Ohms 20 Ohms 26.67 Ohms


Ee204 01 DC Review

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