A 48 volt source is required to furnish 192 watts to a parallel circuit consisting of 3 resistors of equal value. What is the value of each resistor?

A 48 volt source is required to furnish 192 watts to a parallel circuit consisting of 3 resistors of equal value. What is the value of each resistor?

• A. 9 ohms
• B. 12 ohms
• C. 36 ohms
• D. 18 ohms

Answer: (C)

In a parallel network of three identical resistors, the total resistance is one-third of a single resistor value. The power delivered by a constant voltage source relates to the total resistance by P = V^2 / R_total. Here the source is 48 V and the power is 192 W, so the total resistance the source “sees” is R_total = V^2 / P = 48^2 / 192 = 2304 / 192 = 12 ohms. Since the three resistors are identical in parallel, their combined resistance is R_total = R / 3, so R = 3 × R_total = 3 × 12 = 36 ohms. Therefore each resistor is 36 ohms. (Optional check: each branch current is 48/36 = 1.333 A, total current ≈ 4 A, and P = 48 V × 4 A = 192 W.)

In a parallel network of three identical resistors, the total resistance is one-third of a single resistor value. The power delivered by a constant voltage source relates to the total resistance by P = V^2 / R_total. Here the source is 48 V and the power is 192 W, so the total resistance the source “sees” is R_total = V^2 / P = 48^2 / 192 = 2304 / 192 = 12 ohms. Since the three resistors are identical in parallel, their combined resistance is R_total = R / 3, so R = 3 × R_total = 3 × 12 = 36 ohms. Therefore each resistor is 36 ohms. (Optional check: each branch current is 48/36 = 1.333 A, total current ≈ 4 A, and P = 48 V × 4 A = 192 W.)