Question

A 5.0 Ω resistor, a 9.0 Ω resistor, and a 12.0 Ω resistor are connected in parallel across a 24.0 V battery.

a) What is the equivalent resistance of the circuit? Answer in units of Ω

b) What is the current in the 5.0 Ω resistor?
Answer in units of A

Answer 1

E = emf = 24V.
R1 = 5 Ohms
R2 = 9 Ohms
R3 = 12 Ohms

a. 1/Req = 1/R1 + 1/R2 + 1/R3
1/Req = 1/5 + 1/9 + 1/12 = 0.3944444
Req = 2.535 Ohms

b. It = I1+I2+I3 = E/Req = 24/2.535 = 9.47A

I2 = 12/9 * I3 = 1.33I3

I1 = 12/5 * I3 = 2.4I3

I3 + 1.33I3 + 2.4I3 = 9.47
4.733I3 = 9.47
I3 = 2.0A

I1 = 2.4*I3 = 2.4 * 2.0 = 4.8A. = Current through the 5 ohm resistor.