A 18V ideal battery is connected to a circuit that splits into two separate branches before recombining.
• Branch 1 consists of a single resistor R1=6Ω.
• Branch 2 consists of two resistors, R2=4Ω followed in series by R3=4Ω.
Assume connecting wires have negligible resistance.
(a) Rank the magnitudes of the currents I1,I2, and I3 through R1,R2, and R3, respectively. Clearly indicate any ties.
(b) Rank the magnitudes of the potential differences ΔV1,ΔV2, and ΔV3 across R1,R2, and R3, respectively. Clearly indicate any ties.
(c) Without performing numerical calculations, justify both rankings using appropriate principles of electric circuits.