Question

if a 12 V battery is connected to the circuit shown, and R1 and R2 are EACH 2 ohm resistors; what must be the resistance of R4 be if R3 is 4 ohms and the total current is 2 amp?

Answer 1

Step-by-step explanation:

First find the total resistance of the combination circuit:

R = V/I = 12 V / 2 A = 6 Ω

6Ω = R1 + R2 + 1/(1/R3 + 1/R4)

6Ω = 2Ω + 2Ω + 1/(1/4 + 1/R4)

2Ω = 1/(1/4Ω + 1/R4)

2Ω(1/4Ω + 1/R4) = 1

(1/4 + 1/R4) = 1/2

1/R4 = 1/4

R4 = 4Ω

Note: R1 and R2 are in series, so you just add them together. But R3 and R4 are in parallel, so Req = 1/R3 + 1/R4