Currents add in parallel

The idea

In a parallel combination each resistor has the same potential difference V across it, and the total current equals the sum of the separate branch currents: I = I1 + I2 + I3.

A road that splits

A 6 V battery is joined to three resistors in parallel. The three branches carry 3 A, 2 A and 1 A.

How large is the total current drawn from the battery?

• 6 A, the sum of the three
• 3 A, the biggest branch current
• 1 A, the smallest branch current

Branches

Press Next step to see the potential difference, the branch currents and the total current.

Same push, shared current

Each resistor had the same potential difference across it. The current split into three branch currents, and together they made the total current.

In a parallel combination each resistor has the same potential difference V across it, and the total current equals the sum of the separate branch currents: I = I₁ + I₂ + I₃.

Notes

In parallel, each resistor has the same potential difference V, and the total current is the sum of the branch currents: I = I₁ + I₂ + I₃.

Check yourself

Three resistors are in parallel. The branch currents are 2.4 A, 1.2 A and 0.4 A. What is the total current, in A?

Answer: 4 A

I = I₁ + I₂ + I₃ = 2.4 A + 1.2 A + 0.4 A = 4 A.

The total current is 6 A. Two of the three branches carry 3 A and 2 A. What current flows in the third branch, in A?

Answer: 1 A

I = I₁ + I₂ + I₃ gives 6 A = 3 A + 2 A + I₃, so I₃ = 1 A.

A 12 V battery is joined to two resistors in parallel. What is the potential difference across each resistor?

Which statement about resistors in parallel is correct?

• 12 V across each — correct. Yes!
• 6 V across each, because it is shared. In a parallel combination each resistor has the same potential difference V across it, the full 12 V here.
• 12 V across one and zero across the other. Both resistors are joined between the same two points, so each has the full 12 V across it.
• The total current is the same as each branch current. Each branch carries a part of the total current, and the parts add up to the total.
• The total current is the sum of the branch currents — correct. Yes!
• The potential differences add up to the total. That is for resistors in series. In parallel every resistor has the same potential difference.