Determine the total resistance in a circuit where the power dissipated is 25 watts and the supplied voltage is 50 volts.

Determine the total resistance in a circuit where the power dissipated is 25 watts and the supplied voltage is 50 volts.

• A. 125 ohms
• B. 100 ohms
• C. 50 ohms
• D. 250 ohms

Answer: (B)

Power dissipated in a resistor depends on the voltage across it and its resistance through P = V^2 / R. Rearranging gives R = V^2 / P. With V = 50 V and P = 25 W, R = 50^2 / 25 = 2500 / 25 = 100 ohms. A quick check: the current would be I = V / R = 50 / 100 = 0.5 A, and P = V × I = 50 × 0.5 = 25 W, which matches. If the resistance were 125 ohms, P would be 2500/125 = 20 W; if 50 ohms, P would be 2500/50 = 50 W; if 250 ohms, P would be 2500/250 = 10 W. So the correct total resistance is 100 ohms.

Power dissipated in a resistor depends on the voltage across it and its resistance through P = V^2 / R. Rearranging gives R = V^2 / P. With V = 50 V and P = 25 W, R = 50^2 / 25 = 2500 / 25 = 100 ohms. A quick check: the current would be I = V / R = 50 / 100 = 0.5 A, and P = V × I = 50 × 0.5 = 25 W, which matches. If the resistance were 125 ohms, P would be 2500/125 = 20 W; if 50 ohms, P would be 2500/50 = 50 W; if 250 ohms, P would be 2500/250 = 10 W. So the correct total resistance is 100 ohms.