high importancemedium difficulty5 min

Parallel Combination

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

In one line: Parallel means many paths, same voltage.

Understand it

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.

Example

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

Formula and rule

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

See it worked out

Follow the example line by line, then use the same method on new questions.

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 you can reuse

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

Sketch it in your answer

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

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

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

Think first, then show answer

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

Common wrong answer

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

Don't mix this up

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

Exam tip

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