In a parallel circuit with four equal resistors powered by 24 V and delivering 48 W total, what is the resistance of each resistor?

In a parallel circuit with four equal resistors powered by 24 V and delivering 48 W total, what is the resistance of each resistor?

• A. 12 ohms
• B. 24 ohms
• C. 48 ohms
• D. 96 ohms

Answer: (C)

In a parallel circuit with identical resistors, the total resistance is reduced by the number of resistors: R_eq = R / n. The source delivers power P = V^2 / R_eq, so you can find the equivalent resistance from the supply voltage and total power. Compute R_eq from P and V: R_eq = V^2 / P = 24^2 / 48 = 576 / 48 = 12 ohms. Since there are four equal resistors in parallel, R_eq = R / 4, so R = 4 × 12 = 48 ohms. Cross-check: each resistor sees the full 24 V, so each has power P_i = V^2 / R = 24^2 / 48 = 12 W. Four resistors give total 48 W, which matches the given total.

In a parallel circuit with identical resistors, the total resistance is reduced by the number of resistors: R_eq = R / n. The source delivers power P = V^2 / R_eq, so you can find the equivalent resistance from the supply voltage and total power.

Compute R_eq from P and V: R_eq = V^2 / P = 24^2 / 48 = 576 / 48 = 12 ohms. Since there are four equal resistors in parallel, R_eq = R / 4, so R = 4 × 12 = 48 ohms.

Cross-check: each resistor sees the full 24 V, so each has power P_i = V^2 / R = 24^2 / 48 = 12 W. Four resistors give total 48 W, which matches the given total.