1. Resistors in Series and Parallel Circuits

2. Resistors in circuits
To determine the current or voltage in a circuit that contains multiple resistors, the total resistance must first be calculated.
Resistors can be combined in series or parallel.

3. Resistors in Series Rt = R1 + R2 + R3 +…
When connected in series, the total resistance (Rt) is equal to:
Rt = R1 + R2 + R3 +…
The total resistance is always larger than any individual resistance.

4. Sample Problem
10 V
15 Ω
10 Ω
6 Ω
Calculate the total current through the circuit.
Rt =
Rt =
I = V/Rt =

5. Sample Problem
10 V
15 Ω
10 Ω
6 Ω
Calculate the total current through the circuit.
Rt = 15 Ω +10 Ω + 6 Ω
Rt =
I = V/Rt

6. Sample Problem
10 V
15 Ω
10 Ω
6 Ω
Calculate the total current through the circuit.
Rt = 15 Ω +10 Ω + 6 Ω
Rt = 31 Ω
I = V/Rt
= 10 V/ 31 Ω =

7. Sample Problem
10 V
15 Ω
10 Ω
6 Ω
Calculate the total current through the circuit.
Rt = 15 Ω +10 Ω + 6 Ω
Rt = 31 Ω
I = V/Rt
= 10 V/ 31 Ω =
0.32 A

8. Resistors in Series 10 V 5 V 3 V 2 V
Since charge has only one path to flow through, the current that passes through each resistor is the same.
The sum of all potential differences equals the potential difference across the battery.
10 V
5 V
3 V
2 V

9. Resistors in Parallel 1/Rt = 1/R1 + 1/R2 + 1/R3 +…
When connected in parallel, the total resistance (Rt) is equal to:
1/Rt = 1/R1 + 1/R2 + 1/R3 +…
Due to this reciprocal relationship, the total resistance is always smaller than any individual resistance.

10. Sample Problem
Calculate the total resistance through this segment of a circuit.
12 Ω
4 Ω
6 Ω
1/Rt = =
1/Rt =
Rt =

11. Sample Problem
Calculate the total resistance through this segment of a circuit.
12 Ω
4 Ω
6 Ω
1/Rt = 1/12 Ω +1/4 Ω + 1/6 Ω =
1/Rt =
Rt =

12. Sample Problem
Calculate the total resistance through this segment of a circuit.
12 Ω
4 Ω
6 Ω
1/Rt = 1/12 Ω +1/4 Ω + 1/6 Ω
= 1/12 Ω + 3/12 Ω + 2/12 Ω
1/Rt =
Rt =

13. Sample Problem
Calculate the total resistance through this segment of a circuit.
12 Ω
4 Ω
6 Ω
1/Rt = 1/12 Ω +1/4 Ω + 1/6 Ω
= 1/12 Ω + 3/12 Ω + 2/12 Ω
1/Rt = 6/12 Ω = ½ Ω
Rt =

14. Sample Problem
Calculate the total resistance through this segment of a circuit.
12 Ω
4 Ω
6 Ω
1/Rt = 1/12 Ω +1/4 Ω + 1/6 Ω
= 1/12 Ω + 3/12 Ω + 2/12 Ω
1/Rt = 6/12 Ω = ½ Ω
Rt = 2 Ω

15. smallest resistor = more current passes
Resistors in Parallel
Since there is more than one possible path, the current divides itself according to the resistance of each path.
smallest resistor = more current passes
largest resistor = least current passes

16. Resistors in Parallel
The voltage across each resistor in a parallel combination is the same.
10 V

17. Calculate the total resistance in the circuit below+ -
3 Ω
2 Ω
6 Ω
4 Ω
Rtot =
Rtot =
Rtot =
1/Rtot =

18. Calculate the total resistance in the circuit below+ -
3 Ω
2 Ω
6 Ω
4 Ω
Rtot = 3 Ω + 2 Ω = 5 Ω
Rtot = 6 Ω + 4 Ω = 10 Ω
Rtot =
1/Rtot =

19. Calculate the total resistance in the circuit below+ -
3 Ω
2 Ω
6 Ω
4 Ω
Rtot = 3 Ω + 2 Ω = 5 Ω
Rtot = 6 Ω + 4 Ω = 10 Ω
Rtot =
1/Rtot = 2/10 Ω+ 1/10 Ω = 3/10 Ω

20. Calculate the total resistance in the circuit below+ -
3 Ω
2 Ω
6 Ω
4 Ω
Rtot = 3 Ω + 2 Ω = 5 Ω
Rtot = 6 Ω + 4 Ω = 10 Ω
Rtot = 3 1/3 Ω
1/Rtot = 2/10 Ω+ 1/10 Ω = 3/10 Ω