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Parallel Combination

In a parallel combination, components are connected in separate branches across the same two points.

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Student-friendly explanation

Each branch gets the same potential difference, but the current splits among the branches. The equivalent resistance becomes less than the resistance of the smallest branch resistor. This arrangement is widely used in home wiring.

How to write this in exams

  1. 1

    Start with the exact idea

    In a parallel combination, components are connected in separate branches across the same two points.

  2. 2

    Then show how to use it

    1. Identify separate branches across the same two points. 2. Keep voltage the same for all branches. 3. Use the reciprocal formula for equivalent resistance. 4. Check that the answer is less than the smallest branch resistance.

  3. 3

    Add one concrete example

    Two bulbs connected in parallel receive the same supply voltage, so each works independently.

  4. 4

    Avoid this incomplete answer

    A common wrong answer is to add the resistances directly. That is only correct for series, not for parallel.

Definition

In a parallel combination, components are connected in separate branches across the same two points.

Example

Two bulbs connected in parallel receive the same supply voltage, so each works independently.

Rule to remember

For parallel resistors, 1/Rp = 1/R1 + 1/R2 + 1/R3 ... and the voltage across each branch is the same.

Memory hook

Parallel means many paths, same voltage.

Examples and method

Worked example

If 6 ohm and 3 ohm resistors are connected in parallel, 1/Rp = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2, so Rp = 2 ohm.

Method to apply

1. Identify separate branches across the same two points. 2. Keep voltage the same for all branches. 3. Use the reciprocal formula for equivalent resistance. 4. Check that the answer is less than the smallest branch resistance.

Diagram support

Draw two or more branches across the same battery terminals and label the voltage across each branch equally.

How CBSE asks it

Commonly asked in numericals on equivalent resistance, or in home wiring questions about why devices are connected in parallel.

Avoid common mistakes

Common confusion

Students often add resistances directly in parallel or think current is the same in every branch.

Common wrong answer

A common wrong answer is to add the resistances directly. That is only correct for series, not for parallel.

Exam tip

Remember parallel means many paths and the same voltage across each branch.

Quick check

What is the potential difference across each branch in a parallel circuit?

The potential difference is the same across each branch because every branch is connected between the same two points of the supply.

Study the parallel combination diagram carefully

Use the labelled diagram to keep parallel combination clear in short answers and revision.

What this diagram makes clear

This diagram keeps the labels and direction of parallel combination in the right order.

Where this helps in exams

Use this for labelled diagram work and short exam answers on parallel combination.

Revision cue

Revise parallel combination through the labels before writing the answer.

Answer writing and exam use

1-mark answer

In a parallel combination, components are connected in separate branches across the same two points.

2-mark answer

In a parallel combination, components are connected in separate branches across the same two points. For parallel resistors, 1/Rp = 1/R1 + 1/R2 + 1/R3 ... and the voltage across each branch is the same. Two bulbs connected in parallel receive the same supply voltage, so each works independently.

3-mark answer

Each branch gets the same potential difference, but the current splits among the branches. The equivalent resistance becomes less than the resistance of the smallest branch resistor. This arrangement is widely used in home wiring. For parallel resistors, 1/Rp = 1/R1 + 1/R2 + 1/R3 ... and the voltage across each branch is the same. If 6 ohm and 3 ohm resistors are connected in parallel, 1/Rp = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2, so Rp = 2 ohm. Commonly asked in numericals on equivalent resistance, or in home wiring questions about why devices are connected in parallel. A common wrong answer is to add the resistances directly. That is only correct for series, not for parallel.
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