Series Circuit Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Series Circuit.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

A circuit arrangement in which components are connected end-to-end along a single path, so exactly the same current flows through every component.

Like cars on a single-lane road — every car (charge) must pass through every toll booth (component) in order.

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How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Series Circuit asks students to follow the circuit path and identify what quantity changes at each component.

Common stuck point: Students often know a formula related to series circuit but skip the recognition step: Can I identify the circuit path, what quantity is flowing or changing, and which electrical rule links the quantities? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Can I identify the circuit path, what quantity is flowing or changing, and which electrical rule links the quantities?

Worked Examples

Example 1

medium
Three resistors (4 Ω4 \text{ } \Omega, 6 Ω6 \text{ } \Omega, 10 Ω10 \text{ } \Omega) are connected in series to a 20 V20 \text{ V} battery. What is the current and the voltage across each resistor?

Answer

I=1 A;V1=4 V,V2=6 V,V3=10 VI = 1 \text{ A}; \quad V_1 = 4 \text{ V}, V_2 = 6 \text{ V}, V_3 = 10 \text{ V}

First step

1
Total resistance: RT=4+6+10=20 ΩR_T = 4 + 6 + 10 = 20 \text{ } \Omega.

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Example 2

hard
A 6 V6 \text{ V} battery powers a series circuit with a 3 Ω3 \text{ } \Omega resistor and an unknown resistor. The current is 0.5 A0.5 \text{ A}. Find the unknown resistance and the power dissipated by each resistor.

Example 3

medium
A 24 V24 \text{ V} battery drives resistors R1=2 ΩR_1 = 2 \text{ } \Omega, R2=4 ΩR_2 = 4 \text{ } \Omega, R3=6 ΩR_3 = 6 \text{ } \Omega in series. Find (a) the current and (b) the voltage across R3R_3.

Example 4

medium
Two old-style filament bulbs rated "2 V,0.3 A2 \text{ V}, 0.3 \text{ A}" are wired in series across a 4 V4 \text{ V} battery. Treating each bulb as a fixed resistor at its rating, will they light at rated brightness? Justify.

Example 5

medium
A 30 V30 \text{ V} source drives resistors R1,R2,R3R_1, R_2, R_3 in series. The voltages across them are in the ratio 1:2:31:2:3. Find each voltage.

Example 6

hard
A series circuit has a 5 Ω5 \text{ } \Omega resistor and a 10 Ω10 \text{ } \Omega resistor across a battery of unknown emf. The 10 Ω10 \text{ } \Omega resistor dissipates 4 W4 \text{ W}. Find the loop current and the emf.

Example 7

hard
Design a voltage divider using two series resistors to drop a 12 V12 \text{ V} source down to 4 V4 \text{ V} across the lower resistor, with a total current of 10 mA10 \text{ mA}.

Example 8

challenge
nn identical resistors RR are connected in series across a fixed voltage VV. Show that the power dissipated by the whole network scales as 1/n1/n.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

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Two resistors in series have a total resistance of 15 Ω15 \text{ } \Omega. If one is 7 Ω7 \text{ } \Omega, what is the other?

Example 2

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Three resistors (4 Ω4 \text{ } \Omega, 6 Ω6 \text{ } \Omega, and 2 Ω2 \text{ } \Omega) are connected in series to a 24 V24 \text{ V} battery. Calculate: (a) total resistance, (b) current, (c) voltage across the 6 Ω6 \text{ } \Omega resistor.

Example 3

easy
How do you find the total resistance of resistors in series?

Example 4

easy
In a series circuit, is the current the same through every component?

Example 5

easy
Resistors 5 Ω5\,\Omega and 7 Ω7\,\Omega are in series. Find the total resistance.

Example 6

easy
In a series circuit, do the voltage drops add up to the source voltage?

Example 7

easy
A 1212 V source drives two equal series resistors. What voltage is across each?

Example 8

easy
Three 2 Ω2\,\Omega resistors are in series. What is the total resistance?

Example 9

easy
If one component in a series circuit breaks (open), what happens to the current?

Example 10

easy
In a series circuit with current 33 A, what current flows through the third resistor?

Example 11

medium
A 2424 V battery drives 4 Ω4\,\Omega and 8 Ω8\,\Omega in series. Find the current and the voltage across the 8 Ω8\,\Omega resistor.

Example 12

medium
A series circuit has 3 Ω3\,\Omega and 6 Ω6\,\Omega resistors and a current of 22 A. What is the source voltage?

Example 13

medium
Three resistors 1 Ω1\,\Omega, 2 Ω2\,\Omega, 3 Ω3\,\Omega are in series with a 1212 V battery. Find the current.

Example 14

medium
In a series circuit, the drops are 44 V and 88 V across two resistors. If the smaller resistor is 2 Ω2\,\Omega, find the current and the larger resistance.

Example 15

medium
A 1010 V source feeds 2 Ω2\,\Omega, 3 Ω3\,\Omega, and 5 Ω5\,\Omega in series. What is the voltage across the 3 Ω3\,\Omega resistor?

Example 16

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A series circuit dissipates power in two resistors 4 Ω4\,\Omega and 6 Ω6\,\Omega with 22 A flowing. What total power is dissipated?

Example 17

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A series voltage divider has R1=3 ΩR_1 = 3\,\Omega and R2=9 ΩR_2 = 9\,\Omega across 2424 V. Find the voltage across R2R_2.

Example 18

challenge
Two resistors in series across 2020 V give drops in the ratio 2:32:3. Find both drops, and if the smaller resistor is 4 Ω4\,\Omega, the current.

Example 19

challenge
A 3030 V source feeds three series resistors. The first drops 66 V, and the remaining two are equal. Find each of the remaining drops.

Example 20

challenge
A series circuit with a 99 V battery and total resistance RR carries 0.60.6 A. A 3 Ω3\,\Omega resistor is then added in series. What is the new current?

Example 21

medium
A 2020 V source drives 5 Ω5\,\Omega and 5 Ω5\,\Omega in series. Find the current.

Example 22

medium
In a series circuit, 22 A flows through a 3 Ω3\,\Omega and a 4 Ω4\,\Omega resistor. Find each voltage drop.

Example 23

easy
Resistors of 3 Ω3 \text{ } \Omega, 4 Ω4 \text{ } \Omega, and 5 Ω5 \text{ } \Omega are in series. What is the total resistance?

Example 24

easy
Four identical 3 Ω3 \text{ } \Omega resistors are in series. What is the total resistance?

Example 25

easy
In a series circuit, V1=4 VV_1 = 4 \text{ V}, V2=5 VV_2 = 5 \text{ V}, V3=7 VV_3 = 7 \text{ V}. What is the supply voltage?

Example 26

easy
Two resistors, 8 Ω8 \text{ } \Omega and 12 Ω12 \text{ } \Omega, are in series with a 10 V10 \text{ V} battery. What is the current?

Example 27

medium
A series circuit has resistors R1=10 ΩR_1 = 10 \text{ } \Omega and R2=20 ΩR_2 = 20 \text{ } \Omega across 30 V30 \text{ V}. What fraction of the supply voltage appears across R2R_2?

Example 28

medium
Three resistors in series share 18 V18 \text{ V}. Two of them are equal and each dissipate 4 V4 \text{ V}. What voltage is across the third resistor?

Example 29

medium
A 12 V12 \text{ V} battery drives a 4 Ω4 \text{ } \Omega resistor in series with an unknown RR. The current is 1.5 A1.5 \text{ A}. Find RR.

Example 30

medium
Two resistors R1=6 ΩR_1 = 6 \text{ } \Omega and R2=9 ΩR_2 = 9 \text{ } \Omega are in series across a 15 V15 \text{ V} battery. What power is dissipated by R2R_2?

Example 31

hard
A wire of resistance 1 Ω1 \text{ } \Omega is added in series to a 9 V9 \text{ V} battery driving a 2 Ω2 \text{ } \Omega load. By what percentage does the power delivered to the load fall compared with no wire resistance?

Example 32

hard
A 6 V6 \text{ V} battery drives resistors R1=2 ΩR_1 = 2 \text{ } \Omega and R2=4 ΩR_2 = 4 \text{ } \Omega in series. The battery has internal resistance 1 Ω1 \text{ } \Omega. Find the terminal voltage of the battery.

Example 33

hard
Three series resistors dissipate 1 W1 \text{ W}, 2 W2 \text{ W}, and 3 W3 \text{ W} respectively. The current is 1 A1 \text{ A}. Find each resistance and the total supply voltage.

Example 34

medium
An ammeter (assume ideal) is inserted into a series circuit with a 10 Ω10 \text{ } \Omega resistor and a 5 V5 \text{ V} source. What does it read?

Example 35

hard
Two batteries of 6 V6 \text{ V} and 9 V9 \text{ V} are connected in series so their emfs add, driving a 5 Ω5 \text{ } \Omega resistor (ignore internal resistance). What current flows?

Example 36

challenge
Old-style Christmas lights have 5050 identical bulbs in series across a 120 V120 \text{ V} supply. Each bulb dissipates 1.2 W1.2 \text{ W} at its operating point. Find the current and the resistance of each bulb at operation.
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Background Knowledge

These ideas may be useful before you work through the harder examples.

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