What is the resistance of each resistor in the 24-volt parallel circuit described to yield a total of 48 watts across four equal resistors?

What is the resistance of each resistor in the 24-volt parallel circuit described to yield a total of 48 watts across four equal resistors?

• A. 48 ohms
• B. 12 ohms
• C. 6 ohms
• D. 24 ohms

Answer: (A)

In a parallel circuit, all resistors share the same supply voltage and the total power is the sum of the power in each branch. With four identical resistors of resistance R across 24 volts, each branch draws P_branch = V^2 / R, so the total power is P_total = 4 V^2 / R. Set this equal to 48 watts and solve for R: 48 = 4*(24^2)/R, so R = 4*(24^2)/48 = 2304/48 = 48 ohms. Therefore, each resistor is 48 ohms. You can also see this by using the equivalent resistance of four equal resistors in parallel, which is R/4, and P = V^2 / (R/4) = 4 V^2 / R, leading to the same result.

In a parallel circuit, all resistors share the same supply voltage and the total power is the sum of the power in each branch. With four identical resistors of resistance R across 24 volts, each branch draws P_branch = V^2 / R, so the total power is P_total = 4 V^2 / R. Set this equal to 48 watts and solve for R: 48 = 4*(24^2)/R, so R = 4*(24^2)/48 = 2304/48 = 48 ohms. Therefore, each resistor is 48 ohms. You can also see this by using the equivalent resistance of four equal resistors in parallel, which is R/4, and P = V^2 / (R/4) = 4 V^2 / R, leading to the same result.