A circuit contains two fixed resistors, R1=100Ω and R2=300Ω, connected in series to an ideal 120V dc power supply. The resistors are thermally insulated so that all electrical energy they receive remains within each resistor as internal energy of their material.
(a) Calculate the current in the circuit.
(b) Determine the rate at which each resistor converts electrical energy into thermal energy.
(c) After the circuit has been operated continuously for 5.0min, calculate the ratio of the thermal energy generated in R2 to that generated in R1. Explain why this ratio has the value you obtained.
(d) Suppose R2 is replaced by a single unknown resistor Rx such that, when placed in series with R1 and connected to the same 120V supply, Rx converts thermal energy at the same rate as R1. Derive an algebraic expression for Rx in terms of R1 and the supply voltage, and calculate its numerical value.