Parallel Circuit Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Parallel 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 in which components are connected across the same two points, so each has the same voltage across it.

Like a river splitting into branches — the water (current) divides, but the pressure drop (voltage) across each branch is the same.

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: Same voltage across each branch, but current splits. Total resistance is less than the smallest branch.

Common stuck point: Adding more resistors in parallel decreases total resistance and increases total current.

Sense of Study hint: When analysing a parallel circuit, remember that voltage is the same across every branch. First, find the current through each branch using Ohm's law (I = V/R). Then add the branch currents to get the total current. To find total resistance, use 1/R_{\text{total}} = 1/R_1 + 1/R_2 + \ldots

Worked Examples

Example 1

medium
Two resistors (6 \text{ } \Omega and 12 \text{ } \Omega) are connected in parallel to a 12 \text{ V} battery. What is the total resistance and the current through each resistor?

Solution

  1. 1
    Total resistance: \frac{1}{R_T} = \frac{1}{6} + \frac{1}{12} = \frac{2}{12} + \frac{1}{12} = \frac{3}{12} \implies R_T = 4 \text{ } \Omega
  2. 2
    Current through 6 \text{ } \Omega: I_1 = \frac{V}{R_1} = \frac{12}{6} = 2 \text{ A}.
  3. 3
    Current through 12 \text{ } \Omega: I_2 = \frac{V}{R_2} = \frac{12}{12} = 1 \text{ A}.
  4. 4
    Total current: I_T = 2 + 1 = 3 \text{ A} (consistent with V/R_T = 12/4 = 3 \text{ A}).

Answer

R_T = 4 \text{ } \Omega; \quad I_1 = 2 \text{ A}, I_2 = 1 \text{ A}
In parallel circuits, voltage is the same across all branches. The total resistance is less than the smallest individual resistance, and more current flows through the smaller resistor.

Example 2

hard
Three identical 30 \text{ } \Omega resistors are connected in parallel. What is the total resistance?

Example 3

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Three resistors of 6 \text{ } \Omega, 12 \text{ } \Omega, and 4 \text{ } \Omega are connected in parallel. Find the total resistance.

Practice Problems

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

Example 1

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A 10 \text{ } \Omega and a 15 \text{ } \Omega resistor are in parallel. What is the combined resistance?

Example 2

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Two resistors (10 \text{ } \Omega and 15 \text{ } \Omega) are connected in parallel across a 30 \text{ V} supply. Find: (a) total resistance, (b) total current, (c) current through each resistor.
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Background Knowledge

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

circuitresistanceohms law