A 9-V battery is hooked up to two resistors in series. One has a resistance of 5 Ω, and the other has a resistance of 10 Ω. Several locations along the circuit are marked with letters, as shown in the figure. Through which resistor is energy being dissipated at the higher rate?
A) the 10-Ω resistor
B) the 5-Ω resistor
C) Energy is being dissipated by both resistors at the same rate.

Question

A 9-V battery is hooked up to two resistors in series. One has a resistance of 5 Ω, and the other has a resistance of 10 Ω. Several locations along the circuit are marked with letters, as shown in the figure. Through which resistor is energy being dissipated at the higher rate? 
A) the 10-Ω resistor 
B) the 5-Ω resistor 
C) Energy is being dissipated by both resistors at the same rate.

Quizplus · Accepted Answer

The rate at which energy is dissipated by a resistor is proportional to the square of the current passing through it, according to the formula P = I^2R, where P is power, I is current, and R is resistance. Since the resistors are in series, the current passing through each resistor is the same. However, the power dissipated by each resistor is proportional to its resistance. Therefore, the resistor with the higher resistance (the 10-Ω resistor) will dissipate energy at a higher rate than the resistor with the lower resistance (the 5-Ω resistor).

A 9-V Battery Is Hooked Up to Two Resistors in Series