Resistors in series and parallel circuits

1. Resistors in Series and Resistors in Series and
Parallel CircuitsParallel Circuits

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

3. Resistors in SeriesResistors in Series
When connected in series, the total When connected in series, the total
resistance (Rt) is equal to:resistance (Rt) is equal to:
Rt = RRt = R11 + R + R22 + R + R3 3 +…+…
The total resistance is always larger The total resistance is always larger
than any individual resistance.than any individual resistance.

4. Sample ProblemSample Problem
10 V
15 Ω 10 Ω 6 Ω
Calculate the total Calculate the total
current through the current through the
circuit.circuit.
Rt = 15 Rt = 15 ΩΩ +10 +10 ΩΩ + 6 + 6 ΩΩ
Rt = 31 Rt = 31 ΩΩ
I = V/RI = V/Rtt= 10 V/ 31 = 10 V/ 31 ΩΩ = =0.32 A0.32 A

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

6. Resistors in ParallelResistors in Parallel
When connected in parallel, the total When connected in parallel, the total
resistance (Rt) is equal to:resistance (Rt) is equal to:
1/Rt = 1/R1/Rt = 1/R11 + 1/R + 1/R22 + 1/R + 1/R33 +… +…
Due to this reciprocal relationship, the Due to this reciprocal relationship, the
total resistance is always smaller than total resistance is always smaller than
any individual resistance.any individual resistance.

7. Sample ProblemSample Problem
12 Ω
4 Ω
6 Ω
Calculate the total Calculate the total
resistance through this resistance through this
segment of a circuit.segment of a circuit.
1/Rt = 1/12 1/Rt = 1/12 ΩΩ +1/4 +1/4 ΩΩ + 1/6 + 1/6 ΩΩ
= 1/12 = 1/12 ΩΩ + 3/12 + 3/12 ΩΩ + 2/12 + 2/12 ΩΩ
1/R1/Rt t = 6/12 = 6/12 ΩΩ = = ½ ½ ΩΩ
Rt = 2 Rt = 2 ΩΩ

8. Since there is more than one possible Since there is more than one possible
path, the current divides itself path, the current divides itself
according to the resistance of each according to the resistance of each
path.path.

smallest resistor = more current passessmallest resistor = more current passes
largest resistor = least current passeslargest resistor = least current passes
Resistors in ParallelResistors in Parallel

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

10. Calculate the total resistance in the Calculate the total resistance in the
circuit belowcircuit below
+-
3 3 ΩΩ 2 2 ΩΩ
6 6 ΩΩ 4 4 ΩΩ
RRtottot = 3 = 3 ΩΩ + 2 + 2 ΩΩ = = 5 5 ΩΩ
RRtottot = 6 = 6 ΩΩ + 4 + 4 ΩΩ = = 10 10 ΩΩ
1/R1/Rtottot = 2/10 = 2/10 ΩΩ+ 1/10 + 1/10 ΩΩ = = 3/10 3/10 ΩΩ
RRtottot = 3 = 3
1/31/3
ΩΩ