# An 18 Ω, 9 Ω, and 6 Ω resistor are connected in parallel to an emf source. A current of 4 A is the 9 Ω resistor. How do you calculate the resistance of the circuit? What is the potential difference across the source?

## How do you calculate the current in each resistor?

Mar 1, 2017

Since they are parallel, the voltage is the same for all resistors.

#### Explanation:

Second question:
$U = {I}_{2} \times {R}_{2} = 4 A \times 9 \Omega = 36 V$

First question:
You could use $\frac{1}{R} = \frac{1}{{R}_{1}} + \frac{1}{{R}_{2}} + \frac{1}{{R}_{3}} = \frac{1}{18} + \frac{1}{9} + \frac{1}{6} = \frac{1}{3} \to R = 3 \Omega$

Or:
You can calculate the currents through the other resistors, add them all up and recalculate the total resistance (voltage already calculated):
${I}_{1} = \frac{U}{{R}_{1}} = \frac{36 V}{18 \Omega} = 2 A$

${I}_{2} = 4 A$ (as given)

${I}_{3} = \frac{U}{{R}_{3}} = \frac{36 V}{6 \Omega} = 6 A$

Now $R = \frac{U}{I} = \frac{36 V}{2 A + 4 A + 6 A} = \frac{36 V}{12 A} = 3 \Omega$