A simple circuit has a 24.0 V battery and resistors of resistance 3.0 Ω, 6.0 Ω, and R all connected in parallel. If the current through the battery is 15.0 A, what is the value of R ?

Question

A 0.9 Ω

B 1.1 Ω

C 7.4 Ω

D 8.0 Ω

Answer 1

Apply Ohms Law: Volts = Amps * Ohms.

First approach:

The three resistors are in parallel so each one has 24 Volts across it.

The 3 ohm resistor will draw 24 Volts / 3 ohms = 8 Amps,

The 6 ohm resistor will draw 24 Volts / 6 ohms = 4 Amps.

The third resistor, R, will therefore draw 15 Amps - 8 Amps - 4 Amps = 3 Amps.

So R = 24 Volts / 3 Amps = 8 ohms.

Second approach:

The total parallel resistance is 24 Volts / 15 Amps = 1.6 ohms

The formula for parallel resistors is 1 / [(1/R1) + (1/R2) + (1/R3) + ...]

Therefore 1/1.6 = 1/R + 1/3 + 1/6

Or 1/R = 1/1.6 - 1/3 - 1/6 = 0.125

So R = 1/(0.125) = 8 ohms.