Series Circuit Examples: 44 Problems with Answers

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 \text{ } \Omega

6 \text{ } \Omega

10 \text{ } \Omega

) are connected in series to a

20 \text{ V}

battery. What is the current and the voltage across each resistor?

Answer

I = 1 A; V_{1} = 4 V, V_{2} = 6 V, V_{3} = 10 V

First step

Total resistance:

R_T = 4 + 6 + 10 = 20 \text{ } \Omega

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Example 2

hard

6 \text{ V}

battery powers a series circuit with a

3 \text{ } \Omega

resistor and an unknown resistor. The current is

0.5 \text{ A}

. Find the unknown resistance and the power dissipated by each resistor.

Example 3

medium

24 \text{ V}

battery drives resistors

R_1 = 2 \text{ } \Omega

R_2 = 4 \text{ } \Omega

R_3 = 6 \text{ } \Omega

in series. Find (a) the current and (b) the voltage across

R_3

Example 4

medium

Two old-style filament bulbs rated "

2 \text{ V}, 0.3 \text{ A}

" are wired in series across a

4 \text{ V}

battery. Treating each bulb as a fixed resistor at its rating, will they light at rated brightness? Justify.

Example 5

medium

30 \text{ V}

source drives resistors

R_1, R_2, R_3

in series. The voltages across them are in the ratio

1:2:3

. Find each voltage.

Example 6

hard

A series circuit has a

5 \text{ } \Omega

resistor and a

10 \text{ } \Omega

resistor across a battery of unknown emf. The

10 \text{ } \Omega

resistor dissipates

4 \text{ W}

. Find the loop current and the emf.

Example 7

hard

Design a voltage divider using two series resistors to drop a

12 \text{ V}

source down to

4 \text{ V}

across the lower resistor, with a total current of

10 \text{ mA}

Example 8

challenge

n

identical resistors

R

are connected in series across a fixed voltage

V

. Show that the power dissipated by the whole network scales as

1/n

Practice Problems

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

Example 1

medium

Two resistors in series have a total resistance of

15 \text{ } \Omega

. If one is

7 \text{ } \Omega

, what is the other?

Example 2

medium

Three resistors (

4 \text{ } \Omega

6 \text{ } \Omega

, and

2 \text{ } \Omega

) are connected in series to a

24 \text{ V}

battery. Calculate: (a) total resistance, (b) current, (c) voltage across the

6 \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\,\Omega

and

7\,\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

12

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

Example 8

easy

Three

2\,\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

3

A, what current flows through the third resistor?

Example 11

medium

24

V battery drives

4\,\Omega

and

8\,\Omega

in series. Find the current and the voltage across the

8\,\Omega

resistor.

Example 12

medium

A series circuit has

3\,\Omega

and

6\,\Omega

resistors and a current of

2

A. What is the source voltage?

Example 13

medium

Three resistors

1\,\Omega

2\,\Omega

3\,\Omega

are in series with a

12

V battery. Find the current.

Example 14

medium

In a series circuit, the drops are

4

V and

8

V across two resistors. If the smaller resistor is

2\,\Omega

, find the current and the larger resistance.

Example 15

medium

10

V source feeds

2\,\Omega

3\,\Omega

, and

5\,\Omega

in series. What is the voltage across the

3\,\Omega

resistor?

Example 16

medium

A series circuit dissipates power in two resistors

4\,\Omega

and

6\,\Omega

with

2

A flowing. What total power is dissipated?

Example 17

medium

A series voltage divider has

R_1 = 3\,\Omega

and

R_2 = 9\,\Omega

across

24

V. Find the voltage across

R_2

Example 18

challenge

Two resistors in series across

20

V give drops in the ratio

2:3

. Find both drops, and if the smaller resistor is

4\,\Omega

, the current.

Example 19

challenge

30

V source feeds three series resistors. The first drops

6

V, and the remaining two are equal. Find each of the remaining drops.

Example 20

challenge

A series circuit with a

9

V battery and total resistance

R

carries

0.6

A. A

3\,\Omega

resistor is then added in series. What is the new current?

Example 21

medium

20

V source drives

5\,\Omega

and

5\,\Omega

in series. Find the current.

Example 22

medium

In a series circuit,

2

A flows through a

3\,\Omega

and a

4\,\Omega

resistor. Find each voltage drop.

Example 23

easy

Resistors of

3 \text{ } \Omega

4 \text{ } \Omega

, and

5 \text{ } \Omega

are in series. What is the total resistance?

Example 24

easy

Four identical

3 \text{ } \Omega

resistors are in series. What is the total resistance?

Example 25

easy

In a series circuit,

V_1 = 4 \text{ V}

V_2 = 5 \text{ V}

V_3 = 7 \text{ V}

. What is the supply voltage?

Example 26

easy

Two resistors,

8 \text{ } \Omega

and

12 \text{ } \Omega

, are in series with a

10 \text{ V}

battery. What is the current?

Example 27

medium

A series circuit has resistors

R_1 = 10 \text{ } \Omega

and

R_2 = 20 \text{ } \Omega

across

30 \text{ V}

. What fraction of the supply voltage appears across

R_2

Example 28

medium

Three resistors in series share

18 \text{ V}

. Two of them are equal and each dissipate

4 \text{ V}

. What voltage is across the third resistor?

Example 29

medium

12 \text{ V}

battery drives a

4 \text{ } \Omega

resistor in series with an unknown

R

. The current is

1.5 \text{ A}

. Find

R

Example 30

medium

Two resistors

R_1 = 6 \text{ } \Omega

and

R_2 = 9 \text{ } \Omega

are in series across a

15 \text{ V}

battery. What power is dissipated by

R_2

Example 31

hard

A wire of resistance

1 \text{ } \Omega

is added in series to a

9 \text{ V}

battery driving a

2 \text{ } \Omega

load. By what percentage does the power delivered to the load fall compared with no wire resistance?

Example 32

hard

6 \text{ V}

battery drives resistors

R_1 = 2 \text{ } \Omega

and

R_2 = 4 \text{ } \Omega

in series. The battery has internal resistance

1 \text{ } \Omega

. Find the terminal voltage of the battery.

Example 33

hard

Three series resistors dissipate

1 \text{ W}

2 \text{ W}

, and

3 \text{ W}

respectively. The current is

1 \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 \text{ } \Omega

resistor and a

5 \text{ V}

source. What does it read?

Example 35

hard

Two batteries of

6 \text{ V}

and

9 \text{ V}

are connected in series so their emfs add, driving a

5 \text{ } \Omega

resistor (ignore internal resistance). What current flows?

Example 36

challenge

Old-style Christmas lights have

50

identical bulbs in series across a

120 \text{ V}

supply. Each bulb dissipates

1.2 \text{ W}

at its operating point. Find the current and the resistance of each bulb at operation.

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Related Concepts

Circuit Resistance Ohm's Law Parallel Circuit Circuit Diagram Kirchhoff's Laws

Background Knowledge

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

circuitresistanceohms law