This document discusses resistors in series and parallel circuits. When resistors are in series, the total resistance is equal to the sum of the individual resistances. When resistors are in parallel, the total resistance is always smaller than any individual resistance and is calculated using reciprocals. The key differences are that current is the same through components in series, but divides according to resistance in parallel, and voltage divides across components in series but is the same across parallel components.

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

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

3. Resistors in SeriesResistors in Series
 When connected in series, the totalWhen connected in series, the total
resistance (Rt) is equal to:resistance (Rt) is equal to:
Rt = RRt = R11 + R+ R22 + R+ R33 +…+…
 The total resistance is always largerThe 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 totalCalculate the total
current through thecurrent through the
circuit.circuit.
Rt = 15Rt = 15 ΩΩ +10+10 ΩΩ + 6+ 6 ΩΩ
Rt = 31Rt = 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 flowSince charge has only one path to flow
through, the current that passes throughthrough, the current that passes through
each resistor is the same.each resistor is the same.
 The sum of all potential differences equalsThe 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 totalWhen 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, theDue to this reciprocal relationship, the
total resistance is always smaller thantotal resistance is always smaller than
any individual resistance.any individual resistance.

7. Sample ProblemSample Problem
12 Ω
4 Ω
6 Ω
Calculate the totalCalculate the total
resistance through thisresistance through this
segment of a circuit.segment of a circuit.
1/Rt = 1/121/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/Rtt = 6/12= 6/12 ΩΩ == ½½ ΩΩ
Rt = 2Rt = 2 ΩΩ

8.  Since there is more than one possibleSince there is more than one possible
path, the current divides itselfpath, the current divides itself
according to the resistance of eachaccording 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 aThe 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 theCalculate the total resistance in the
circuit belowcircuit below
+ -
33 ΩΩ 22 ΩΩ
66 ΩΩ 44 ΩΩ
RRtottot = 3= 3 ΩΩ + 2+ 2 ΩΩ == 55 ΩΩ
RRtottot = 6= 6 ΩΩ + 4+ 4 ΩΩ == 1010 ΩΩ
1/R1/Rtottot = 2/10= 2/10 ΩΩ+ 1/10+ 1/10 ΩΩ == 3/103/10 ΩΩ
RRtottot = 3= 3 1/31/3
ΩΩ