Resistors in series and parallel circuits

Resistors in Series Resistors in Series and Parallel Circuitsand Parallel Circuits

Resistors in circuitsResistors in circuits

To determine the current or To determine the current or voltage in a circuit that voltage in a circuit that contains multiple resistors, contains multiple resistors, the total resistance must first the total resistance must first be calculated.be calculated.

Resistors can be combined in Resistors can be combined in series or parallel.series or parallel.

Resistors in SeriesResistors in Series

When connected in series, the When connected in series, the total resistance (Rt) is equal to:total resistance (Rt) is equal to:

Rt = RRt = R11 + R + R22 + R + R3 3 +…+…

The total resistance is always The total resistance is always larger than any individual larger than any individual resistance.resistance.

Sample Sample ProblemProblem

10 V

15 Ω

10 Ω

6 ΩCalculate the Calculate the total current total current through the through the circuit.circuit.Rt = 15 Rt = 15 ΩΩ +10 +10 ΩΩ + + 6 6 ΩΩRt = 31 Rt = 31 ΩΩ

I = I = V/RV/Rtt

= 10 V/ 31 = 10 V/ 31 ΩΩ = =

0.32 0.32 AA

Since charge has only one path to Since charge has only one path to flow through, the current that passes flow through, the current that passes through each resistor is the same.through each resistor is the same.

The sum of all potential differences The sum of all potential differences equals the potential difference equals the potential difference across the battery. across the battery.

Resistors in SeriesResistors in Series

10 V

5 V

3 V

2 V

> R value = > V > R value = > V ValueValue

Resistors in ParallelResistors in Parallel

When connected in parallel, the When connected in parallel, the total resistance (Rt) is equal to:total resistance (Rt) is equal to:

1/Rt = 1/R1/Rt = 1/R11 + 1/R + 1/R22 + 1/R + 1/R33 +… +…

Due to this reciprocal Due to this reciprocal relationship, the total relationship, the total resistance is always smaller resistance is always smaller than any individual resistance.than any individual resistance.

Sample Sample ProblemProblem

12 Ω

4 Ω

6 Ω

Calculate the total Calculate the total resistance through resistance through this segment of a this segment of a circuit.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 ΩΩ1/R1/Rt t = 6/12 = 6/12 ΩΩ = = ½ ½ ΩΩ

Rt = 2 Rt = 2 ΩΩ

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

smallest resistor = more current smallest resistor = more current

passespasses

largest resistor = least largest resistor = least current passescurrent passes


The voltage across each The voltage across each resistor in a parallel resistor in a parallel combination is the same. combination is the same.


10 V

10 V

10 V

10 V

Calculate the total Calculate the total resistance in the circuit resistance in the circuit

belowbelow

+ -

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

Engineering

Resistors in series and parallel circuits