The best way to get comfortable with electrical circuit calculations is to just do them! We've made a super easy version of the series circuit puzzles. No calculator required! You can check each answer immediately to make sure you're on the right track.

- Remember that current is the same at all points, and through each load in a series circuit.
- Assume that the components in each circuit function correctly.
- Fuses and closed switches have a resistance of 0 Ω.

In **Basic Electrical Concepts**, you were introduced to a couple of very handy formulas. You'll need them, as well as the concepts from the **Series and Parallel Basics** lesson, to solve these puzzles.

Formula Term | Unit |
---|---|

Current (I) | amps (A) |

Power (P) | watts (W) |

Resistance (R) | ohms (Ω) |

Voltage (V) | volts (V) |

Can you type in the missing values? Pay attention to the units!

What is the voltage drop across Resistor 1?

12 V

Battery

Battery

12 V

Battery

Battery

Resistor 1

3 Ω

Lamp

Lamp

Total Circuit Resistance: 12 Ω

Circuit Current:

12 V

Battery

Battery

12 V

Battery

Battery

0 Ω

Fuse

Fuse

4 Ω

Lamp

Lamp

8 Ω

Solenoid

Solenoid

Total Circuit Resistance:

Circuit Current:

How about this circuit? Enter the missing values.

What is the voltage drop across the solenoid?

How much power is the lamp using?

Circuit Current:

If the switch is opened, how many watts will the motor use?

0 Ω Fuse

10 Ω

Motor

Motor

2 Ω

Resistor

Resistor

0 Ω

Level Switch

Level Switch

12 V

Battery

Battery

12 V

Battery

Battery

0 Ω

Switch

Switch

4 V

Lamp 1

Lamp 1

6 Ω

Lamp 2

Lamp 2

Resistor 1

10 Ω

Resistor 2

Resistor 2

(when switch is toggled as shown in schematic)

Want to see how we suggest solving those puzzles? Read on for a detailed walkthrough of each puzzle.

What is the voltage drop across Resistor 1?

Resistance of Resistor 1

- We know that the total resistance

of the circuit is 12 Ω. - Since total resistance in a series circuit

is the sum of each individual resistance,

we can subtract the other resistances

from the total to find the answer.

Total Ω - Lamp Ω = Resistor 1 Ω

12 Ω - 3 Ω = 9 Ω

12 V

Battery

Battery

12 V

Battery

Battery

Resistor 1

3 Ω

Lamp

Lamp

Total Circuit Resistance: 12 Ω

Circuit Current: ?

What is the voltage drop across Resistor 1?

Circuit Current

- Use Ohm's Law

V ÷ R = I

24 V ÷ 12 Ω = 2 A

12 V

Battery

Battery

12 V

Battery

Battery

Resistor 1

3 Ω

Lamp

Lamp

Total Circuit Resistance: 12 Ω

Circuit Current:

What is the voltage drop across Resistor 1?

Voltage Drop Across Resistor 1

- Recall that current is the same

at all points in a series circuit. - Use Ohm's Law

Resistance x Current = Voltage

9 Ω x 2 A = 18 V

12 V

Battery

Battery

12 V

Battery

Battery

Resistor 1

3 Ω

Lamp

Lamp

Total Circuit Resistance: 12 Ω

Circuit Current:

According to Ohm's Law,

current increases as circuit

resistance decreases.

12 V

Battery

Battery

12 V

Battery

Battery

0 Ω

Fuse

Fuse

4 Ω

Lamp

Lamp

8 Ω

Solenoid

Solenoid

Total Circuit Resistance:

Circuit Current: ?

What is the voltage drop across the solenoid?

How much power is the lamp using?

Total Circuit Resistance

Total series circuit resistance = sum of all circuit resistances.

Fuse Ω + Lamp Ω + Solenoid Ω = Total Ω

0 Ω + 4 Ω + 8 Ω = 12 Ω

12 V

Battery

Battery

12 V

Battery

Battery

0 Ω

Fuse

Fuse

4 Ω

Lamp

Lamp

8 Ω

Solenoid

Solenoid

Total Circuit Resistance:

Circuit Current:

What is the voltage drop across the solenoid?

How much power is the lamp using?

Circuit Current

- Add the two 12 V Battery voltages together to get the total circuit voltage. (24 V)
- Add the resistances together to get the total circuit resistance. (12 Ω)
- Use Ohm's Law.

Volts ÷ Ohms = Amps

24 V ÷ 12 Ω = 2 A

12 V

Battery

Battery

12 V

Battery

Battery

0 Ω

Fuse

Fuse

4 Ω

Lamp

Lamp

8 Ω

Solenoid

Solenoid

Total Circuit Resistance:

Circuit Current:

What is the voltage drop across the solenoid?

How much power is the lamp using?

Voltage Drop Across Solenoid

- Current is the same everywhere in a series circuit.
- Use Ohm's Law and the circuit current.

Ohms x Amps = Volts

8 Ω x 2 A = 16 V

12 V

Battery

Battery

12 V

Battery

Battery

0 Ω

Fuse

Fuse

4 Ω

Lamp

Lamp

8 Ω

Solenoid

Solenoid

Total Circuit Resistance:

Circuit Current:

What is the voltage drop across the solenoid?

How much power is the lamp using?

How much power is the Lamp using?

- The formula for Power is found in the Basic Electrical Units lesson. (P = V x I)
- Voltage drop over the lamp can be determined by subtracting the

solenoid voltage drop from the total voltage, or using Ohm's law.

Ohms x Amps = Volts OR V_{total} - V_{solenoid} = V_{Lamp}

4 Ω x 2 A = 8 V OR 24 V - 16 V = 8 V

8 V x 2 A = 16 W

0 Ω Fuse

10 Ω

Motor

Motor

2 Ω

Resistor

Resistor

0 Ω

Level Switch

Level Switch

12 V

Battery

Battery

?

?

Circuit Resistance: Circuit Current: ?

Circuit Resistance

- Add series resistances together

for total circuit resistance.

0 Ω + 10 Ω + 0 Ω + 2 Ω = 12 Ω

0 Ω Fuse

10 Ω

Motor

Motor

2 Ω

Resistor

Resistor

0 Ω

Level Switch

Level Switch

12 V

Battery

Battery

?

?

Circuit Resistance: Circuit Current:

Circuit Current

- Use Ohm's Law

Volts ÷ Ohms = Amps

12 V ÷ 24 Ω = 0.5 A

0 Ω Fuse

10 Ω

Motor

Motor

2 Ω

Resistor

Resistor

0 Ω

Level Switch

Level Switch

12 V

Battery

Battery

Voltage Drops

- Use Ohm's Law

Ohms x Amps = Volts

0 Ω x 0.5 A = 0 V

20 Ω x 0.5 A= 10 V

If the switch is opened, how many watts will the motor use?

The circuit will become open if the switch

is opened. The motor will not operate and so

will not use power. The answer is 0 Watts.

12 V

Battery

Battery

0 Ω

Switch

Switch

4 V

Lamp 1

?

Lamp 1

?

6 Ω

Lamp 2

Lamp 2

Resistor 1

10 Ω

Resistor 2

Resistor 2

(when switch is toggled as shown in schematic)

Resistor 1 Resistance

- Use Ohm's Law to find the total

circuit resistance.

Volts ÷ Amps = Ohms

12 V ÷ 0.5 mA = 24 Ω

- Now subtract the other resistances

in the circuit from the total, to find

the value for Resistor 1.

24 Ω - 0 Ω - 6 Ω - 10 Ω = 8 Ω

The circuit resistance changes when the

switch is toggled. The original current value can't be used

in this scenario.

Circuit Current

- Use Kirchoff's Voltage Law to solve

for the voltage drop across Resistor 1.

12 V - 4 V = 8 V

- Now solve for current, using Ohm's Law.

Volts ÷ Ohms = Amps

8 V ÷ 8 Ω = 1 mA

12 V

Battery

Battery

0 Ω

Switch

Switch

V

Lamp 1

Lamp 1

6 Ω

Lamp 2

Lamp 2

Resistor 1

10 Ω

Resistor 2

Resistor 2

Solve for Lamp 1 Resistance

- Use Ohm's Law.

Volts ÷ Amps = Ohms

4 V ÷ 1 mA = 4 Ω

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