Chapter 35

Worksheet: Circuits and Ohm’s Law

EQUATIONS

ELECTRICAL CIRCUIT SYMBOLS

1. Draw a circuit schematic (diagram) to include a 50.0 V battery, an ammeter, and a resistance of 10.0 Ω in series.

A

50.0 V 10.0 Ω

+

-

a. What is the reading on the ammeter?

A

50.0 V 10.0 Ω

+

-

R

VI A

VI 5

0.10

50

b. In which direction is the current flowing?

A

50.0 V 10.0 Ω

+

-

Electron flow (-)

Conventional current (+)

2. How much current flows through a radio speaker that has a resistance of 4.0 Ω when 16 V is impressed across the speaker?

R

VI A

VI 0.4

0.4

16

Draw a circuit diagram of the circuit described in the question above. Include a 6 V battery, an ammeter (labeled with value of current), and a resistance of 3.0 Ω (the speaker). Also label the direction of the conventional (+) current.

A

6 V 3.0 Ω

+

-

Conventional current

R

VI

3

6VI AI 2

2 A

4. The following questions pertain to the circuit diagramed to the right.

a. Lamp A reads a voltage of 12 V. What is the voltage of lamp B?

4. The following questions pertain to the circuit diagramed to the right.

a. Lamp A reads a voltage of 12 V. What is the voltage of lamp B?

Since this is a parallel circuit, the voltage in each branch of the circuit is equal to the voltage source.

Therefore, Voltage is equal to 12 volts in each lamp

......321 VVVVs

b. If the ammeters on both branches read the same amount, what does this tell you about the resistance of the two branches?

b. If the ammeters on both branches read the same amount, what does this tell you about the resistance of the two branches?

Since this is parallel circuit, the resistance in each branch can be calculated with the following equation:

Since the voltage and current are the same in each branch, the resistance will be the same

AA R

VI

AA I

VR Rearrange and get

c. If the current flowing in the first branch was 4.0 A and 6.0 A in the second branch, what would the total current in the circuit be?

c. If the current flowing in the first branch was 4.0 A and 6.0 A in the second branch, what would the total current in the circuit be?

Total current in a parallel circuit can be calculated with the following equation:

......CBA IIII

AAI 0.60.4 AI 10

5. Draw a series circuit diagram showing a 6.0 V battery, a resistor, & an ammeter reading of 2.0 A.

A

6.0 V

2.0 A

a. Label: the size of the resistor, the direction of conventional current, the (+) and (-) terminals of the battery.

A

6.0 V

2.0 A

a. Label: the size of the resistor, the direction of conventional current, the (+) and (-) terminals of the battery.

A

6.0 V

2.0 A

+

-

Conventional current

R

VI s

I

VR s 3

0.2

0.6

A

VR

3 Ω

b. Add a voltmeter to you diagram and indicate the potential difference across the resistor.

A

6.0 V

2.0 A

V

.....321 VVVVs

6.0 V

Therefore Vs = V1 = 6.0 V

6. Draw a circuit diagram showing a heater with a resistance of 6 Ω, and a potential difference source of 24.0 V.

A

24.0 V

V 6Ω

a. Calculate the current through the resistance

A

24.0 V

V 6Ω

R

VI s

6

0.24 VI AI 0.4

b. What thermal energy is supplied by the heater in 10 seconds? (HINT- use the equationE = I2Rt to determine energy)

A

24.0 V

V 6Ω

RtIE 2 sAE 100.60.4 2 JE 960

7. Use the circuit diagram to the right to answer the following questions.

a. What is the current flowing through this series circuit if the total resistance is 20 Ω?

R

VI s

20

24VI AI 2.1

b. What would the voltage across each of the three bulbs be? What could you say about the brightness of each of the bulbs?

.....321 VVVVs VVVV 88824

Therefore each bulb would have 8 volts and the same brightness

c. If two of the bulbs had a total resistance of 15 Ω, what would the resistance of the third bulb be?

R

VI s

If the total resistance equals 20 ohms, then the remaining resistor would have a value of 5 ohms

(20 – 15 = 5)

R

VA

0.242.1

A

VR

2.1

0.24

20R

d. What would be the current flowing through the circuit be is the voltage source was 6.0 V, and each of the lamps had a resistance of 2 Ω?

R

VI s

6.0V2Ω

2Ω

2Ω

CBA RRRR First calculate total resistance

Then plug into equation for current

6222R

AV

I 16

6

8. Draw a circuit diagram showing three 10 Ω resistors connected in parallel and placed across a 60.0 V battery.

A

60.0 V

10Ω10Ω 10Ω

a. What is the equivalent resistance of theparallel circuit?

A

60.0 V

10Ω10Ω 10Ω

CBA RRRR

1111

10

1

10

1

10

11

R 10

31

R

Cross multiply and get 103 R 3.3R

b. What is the current through the entire circuit?

A

60.0 V

10Ω10Ω 10Ω

R= 3.3 Ω (from earlier problem) R

VI A

VI 18

3.3

0.60

c. What is the current through each branch ofthe circuit?

A

60.0 V

10Ω10Ω 10Ω

AA R

VI A

VI A 0.6

10

0.60

Since the voltage and resistance are the same in each branch they would have the same current

9. Draw a circuit diagram showing the following: a 800.0 Ω resistor, a 40 Ω resistor, and a 20 Ω resistor connected in parallel and connected across a 24.0 V battery.

A

24.0 V

40Ω800Ω 20Ω

a. What is the equivalent resistance of theparallel circuit?

A

24.0 V

40Ω800Ω 20Ω

CBA RRRR

1111

20

1

40

1

800

11

R 800

611

R

Cross multiply and get 80061 R 13R

b. What is the current through the entire circuit?

A

24.0 V

40Ω800Ω 20Ω

From above problem

13R R

VI A

VI 9.1

13

0.24

c. What is the current through each branch ofthe circuit?

A

24.0 V

40Ω800Ω 20Ω

AA R

VI A

VI A 03.0

800

0.24

AV

IB 6.040

0.24

A

VIC 2.1

20

0.24

10. Answer the following questions about the circuit to the right.

a. What do each of the 4 voltmeters read?

In a parallel circuit, the voltage is the same through each branch and divided by the number of resistors in each branch. Therefore:

VA = 6 V

VB = 6 V

VC = 3 V and VD = 3 V (voltage is split between the two resistors in that branch

6V

b. If each of the resistors are identical, and the total current flowing through this parallel circuit is 12.0 A, what is the total resistance of this circuit?

R

VI

I

VR 5.0

0.12

0.6

A

VR

6V