Resistance Examples in Physics

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

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 measure of how strongly a material opposes electric current, measured in ohms (Ω\Omega) — higher resistance means less current for a given voltage.

Resistance is like friction for electricity — a narrow pipe resists water flow more than a wide one.

Read the full concept explanation →

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: Resistance 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 resistance 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?

Common Mistakes to Watch For

Before you work through the examples, skim the mistake guide so you know which shortcuts and sign errors to avoid.

Electric Current Mistakes

Worked Examples

Example 1

easy
A resistor carries 2 A2 \text{ A} of current when 10 V10 \text{ V} is applied across it. What is the resistance?

Answer

R=5 ΩR = 5 \text{ } \Omega

First step

1
Use Ohm's law rearranged for resistance: R=VIR = \frac{V}{I}.

Full solution

  1. 2
    Substitute the values: R=102R = \frac{10}{2}.
  2. 3
    R=5 ΩR = 5 \text{ } \Omega
Resistance measures how much a component opposes the flow of current. Higher resistance means less current for the same voltage.

Example 2

medium
A wire has length 2 m2 \text{ m}, cross-sectional area 1×10−6 m21 \times 10^{-6} \text{ m}^2, and resistivity ρ=1.7×10−8 Ω⋅m\rho = 1.7 \times 10^{-8} \text{ } \Omega \cdot \text{m} (copper). What is its resistance?

Example 3

medium
Three identical 9 Ω9 \text{ }\Omega resistors are connected in parallel. Find ReqR_{eq}.

Example 4

hard
A wire of resistance 8 Ω8 \text{ }\Omega is stretched uniformly to twice its original length. Find its new resistance (assume volume constant).

Example 5

medium
In the circuit, 6 V6 \text{ V} supplies a 2 Ω2 \text{ }\Omega resistor in series with a parallel pair of 4 Ω4 \text{ }\Omega and 4 Ω4 \text{ }\Omega resistors. Find the total current from the battery.

Example 6

hard
Find the equivalent resistance between A and B: R1=4 ΩR_1 = 4 \text{ }\Omega in series with the parallel combination of R2=6 ΩR_2 = 6 \text{ }\Omega and (R3=3 ΩR_3 = 3 \text{ }\Omega in series with R4=3 ΩR_4 = 3 \text{ }\Omega).

Example 7

medium
Two resistors RR and 2R2R are connected in parallel, then in series with a third resistor RR. Express ReqR_{eq} in terms of RR.

Example 8

hard
A 10 V10 \text{ V} source connects to two parallel branches: branch 1 has 5 Ω5 \text{ }\Omega, branch 2 has 20 Ω20 \text{ }\Omega. Find the current in each branch.

Example 9

challenge
Twelve identical 1 Ω1 \text{ }\Omega resistors are arranged along the edges of a cube. Find the resistance between two opposite corners (body diagonal).

Example 10

medium
The resistance of a tungsten filament rises from 50 Ω50 \text{ }\Omega cold to 500 Ω500 \text{ }\Omega hot. By what factor does the current drop at constant voltage when it warms up?

Example 11

hard
A nichrome wire (ρ=1.1×10−6 Ω⋅m\rho = 1.1 \times 10^{-6} \text{ }\Omega\cdot\text{m}) is needed to make a 5 Ω5 \text{ }\Omega resistor with cross-sectional area 0.5 mm20.5 \text{ mm}^2. What length is required?

Example 12

medium
A 12 V12 \text{ V} battery drives 4 A4 \text{ A} through resistor RR. When a second resistor of 1 Ω1 \text{ }\Omega is added in series, find the new current.

Practice Problems

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

Example 1

easy
If the resistance of a wire doubles and the voltage stays the same, what happens to the current?

Example 2

medium
A wire has resistance R=ρLAR = \rho \frac{L}{A}. If you replace a wire with one that is twice as long and has three times the cross-sectional area (same material), how does the resistance change?

Example 3

easy
What is the SI unit of resistance?

Example 4

easy
Write the formula for resistance in terms of resistivity, length, and area.

Example 5

easy
Does a thicker wire (larger cross-section) have more or less resistance?

Example 6

easy
A resistor has 1212 V across it and 33 A through it. What is its resistance?

Example 7

easy
If you double the length of a wire (same material and area), what happens to its resistance?

Example 8

easy
What is the difference between resistance and resistivity?

Example 9

easy
A 2 Ω2\,\Omega and a 3 Ω3\,\Omega resistor are in series. What is the total resistance?

Example 10

easy
Two equal 4 Ω4\,\Omega resistors are in parallel. Is the total more or less than 4 Ω4\,\Omega?

Example 11

medium
A wire has resistance 6 Ω6\,\Omega. It is stretched to twice its length (area halves, volume constant). What is the new resistance?

Example 12

medium
A material has resistivity 2×10−8 Ω⋅2\times10^{-8}\,\Omega\cdotm. A wire is 44 m long with cross-section 2×10−62\times10^{-6} m2^2. Find its resistance.

Example 13

medium
Three resistors 2 Ω2\,\Omega, 4 Ω4\,\Omega, 6 Ω6\,\Omega are in series. What is the total resistance?

Example 14

medium
Two resistors 6 Ω6\,\Omega and 3 Ω3\,\Omega are in parallel. Find the total resistance.

Example 15

medium
For the product-over-sum shortcut, two parallel resistors 5 Ω5\,\Omega and 20 Ω20\,\Omega give what total?

Example 16

medium
A heater wire is replaced by one of the same material and length but half the cross-sectional area. How does its resistance change?

Example 17

medium
A resistor's current is 0.250.25 A when 55 V is applied. What is its resistance, in ohms?

Example 18

challenge
A wire of resistance RR is cut into three equal pieces, which are then connected in parallel. What is the new total resistance in terms of RR?

Example 19

challenge
A 4 Ω4\,\Omega resistor is in series with a parallel combination of 6 Ω6\,\Omega and 12 Ω12\,\Omega. Find the total resistance.

Example 20

challenge
A wire's resistance is 10 Ω10\,\Omega at 20°20°C. Its resistance rises 0.4%0.4\% per degree. What is its resistance at 70°70°C?

Example 21

medium
Two resistors 8 Ω8\,\Omega and 8 Ω8\,\Omega are in parallel. Find the total resistance.

Example 22

medium
A wire of length LL has resistance 5 Ω5\,\Omega. What is the resistance of a 3L3L wire of the same material and area?

Example 23

easy
A 9 V9 \text{ V} battery drives 3 A3 \text{ A} through a resistor. Find the resistance.

Example 24

medium
Two resistors of 6 Ω6 \text{ }\Omega and 3 Ω3 \text{ }\Omega are connected in parallel. Find the equivalent resistance.

Example 25

easy
A current of 0.5 A0.5 \text{ A} flows through a 24 Ω24 \text{ }\Omega resistor. What voltage drop appears across it?

Example 26

medium
A copper wire has length 5 m5 \text{ m}, cross-section 2×10−6 m22 \times 10^{-6} \text{ m}^2, and resistivity 1.7×10−8 Ω⋅m1.7 \times 10^{-8} \text{ }\Omega\cdot\text{m}. Find its resistance.

Example 27

easy
A 20 Ω20 \text{ }\Omega resistor and 30 Ω30 \text{ }\Omega resistor are in series. The current through the 20 Ω20 \text{ }\Omega resistor is what fraction of the current through the 30 Ω30 \text{ }\Omega resistor?

Example 28

medium
A resistor dissipates 50 W50 \text{ W} when 10 V10 \text{ V} is across it. What is its resistance?

Example 29

medium
An aluminum wire has ρ=2.65×10−8 Ω⋅m\rho = 2.65 \times 10^{-8} \text{ }\Omega\cdot\text{m}, length 10 m10 \text{ m}, and area 1 mm2=10−6 m21 \text{ mm}^2 = 10^{-6} \text{ m}^2. Find the resistance.

Example 30

easy
A bulb labeled 60 W,120 V60 \text{ W}, 120 \text{ V} has what resistance when operating?

Example 31

medium
A heater draws 10 A10 \text{ A} from a 220 V220 \text{ V} supply. Find its resistance.

Example 32

easy
Find the resistance of a circuit element where V=5 VV = 5 \text{ V} and I=0.25 AI = 0.25 \text{ A}.

Example 33

medium
Two resistors 12 Ω12 \text{ }\Omega and 4 Ω4 \text{ }\Omega are in parallel. Find the equivalent resistance.
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Background Knowledge

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

electric currentvoltage