First question (upper left): 1/Req = 1/12 + 1/24 = 1/8 Req = 8 ohms Voltage is equal through different resistors, and V1 = V2 = 24 V. Current varies through parallel resistors: I1 = V1/R1 = 24/12 = 2 A. I2 = 24/24 = 1 A.
Second question (middle left): V1 = V2 = 6 V (parallel circuits) I1 = 2 A, I2 = 1 A, IT = 2+1 = 3 A. R1 = V1/I1 = 6/2 = 3 ohms, R2 = 6/1 = 6 ohms, 1/Req = 1/2 + 1/1, Req = 2/3 ohms
Third question (bottom left): V1 = V2 = 12 V IT = 3 A, meaning Req = V/It = 12 V/3 A = 4 ohms 1/Req = 1/R1 + 1/R2, 1/4 = 1/12 + 1/R2, R2 = 6 ohms I1 = V/R1 = 1 A, I2 = V/R2 = 2 A
Fourth question (top right): 1/Req = 1/20 + 1/20, Req = 10 ohms IT = 4 A, so VT = IT(Req) = 4*10 = 40 V Parallel circuits, so V1 = V2 = VT = 40 V Since the resistors are identical, the current is split evenly between both: I1 = I2 = IT/2 = 2 A.
Fifth question (middle right): 1/Req = 1/5 + 1/20 + 1/4, Req = 2 ohms IT = VT/Req = 40 V/2 ohms = 20 A V1 = V2 = V3 = 40 V The current of 20 A will be divided proportionally according to the resistances of 5, 20, and 4, the factors will be 5/(5+20+4), 20/(5+20+4), and 4/(5+20+4), which are 5/29, 20/29, and 4/29. I1 = 20(5/29) = 100/29 A I2 = 20(20/29) = 400/29 A I3 = 20(4/29) = 80/29 A
Sixth question (bottom right): V2 = 30V is given, but since these are parallel circuits, V1 = VT = 30 V. Then I1 = V1/R1 = 30 V/10 ohms = 3 A. I2 = 30 V/15 ohms = 2 A. IT = 3 + 2 = 5 A 1/Req = 1/10 + 1/15, Req = 6 ohms
