An ideal 18 V battery is connected to two resistors in series: R1 = 30 Ω followed by R2 = 60 Ω. A bypass switch Sb is wired directly in parallel across R2 so that, when Sb is closed, the current can flow around R2 without passing through it. All wires have negligible resistance.
Analyze the circuit for the two positions of Sb described below.
(a) Sb is open. Determine the current supplied by the battery and the potential difference across each resistor.
(b) Sb is closed. Determine the new current in the circuit and the potential difference across R1 and R2.
(c) Compute the ratio of the total electrical power dissipated in the circuit when Sb is closed to the power dissipated when Sb is open. Interpret this ratio in terms of the physical changes produced by closing the bypass switch.