A parallel example

Three parts, and the third is the one that uses what the last page said about every branch sharing the same voltage.

The problem

The figure shows a system of a 12 Ω resistor and a 6 Ω resistor fitted in parallel across a 6 V supply.

Find the equivalent resistance of the system.
Find the current flowing in the system.
What is the current through each resistor?

Figure to be added

Figure for example 1 — a 12 ohm resistor and a 6 ohm resistor drawn on two separate branches between the same pair of points, with a 6 V cell across them.

Part 1 — the equivalent resistance

1 ÷ R = 1 ÷ 12 + 1 ÷ 6

1 ÷ R = 1 ÷ 12 + 2 ÷ 12 = 3 ÷ 12

R = 4 Ω

Part 2 — the current in the system

I = V ÷ R = 6 ÷ 4

= 1.5 A

Part 3 — the current in each branch

Each resistor has the full 6 V across it, because both are joined between the same two points.

through the 12 Ω = 6 ÷ 12 = 0.5 A

through the 6 Ω = 6 ÷ 6 = 1 A

Check it: the branch currents add up

0.5 A + 1 A = 1.5 A, which is the total found in part 2. That is not a coincidence — it is the fact the whole parallel rule was derived from, and it makes a free check on every answer.