Four 1000-ohm resistors are in parallel across 100V AC. What is the power dissipated by one resistor?

Four 1000-ohm resistors are in parallel across 100V AC. What is the power dissipated by one resistor?

• A. 1W
• B. 10W
• C. 100W
• D. 20W

Answer: (B)

In a parallel circuit, every resistor experiences the same voltage across it, so each 1 kΩ resistor sees 100 V (use the RMS value for AC power calculations). The power dissipated by one resistor is P = V^2 / R. Plugging in the numbers: P = 100^2 / 1000 = 10 W. For context, the total power in the branch would be four times that, since each resistor draws the same power, giving 40 W in total (I per resistor is 100 V / 1000 Ω = 0.1 A, and total current is 0.4 A; P_total = V × I_total = 100 × 0.4 = 40 W).

In a parallel circuit, every resistor experiences the same voltage across it, so each 1 kΩ resistor sees 100 V (use the RMS value for AC power calculations). The power dissipated by one resistor is P = V^2 / R. Plugging in the numbers: P = 100^2 / 1000 = 10 W.

For context, the total power in the branch would be four times that, since each resistor draws the same power, giving 40 W in total (I per resistor is 100 V / 1000 Ω = 0.1 A, and total current is 0.4 A; P_total = V × I_total = 100 × 0.4 = 40 W).