Four 100 Ω resistors in series with a 40 V supply: what is the power dissipated by one resistor?

Four 100 Ω resistors in series with a 40 V supply: what is the power dissipated by one resistor?

• A. 0.25 W
• B. 1 W
• C. 2 W
• D. 4 W

Answer: (B)

In a series circuit, the same current flows through every resistor and the total resistance is the sum of the individual resistances. Four 100-ohm resistors give 400 ohms, so the current from a 40 V source is 40/400 = 0.1 A. This current is the same through each resistor, so each one drops 10 V (I × R = 0.1 A × 100 Ω = 10 V). The power in one resistor is P = V × I = 10 V × 0.1 A = 1 W (also P = I^2R = (0.1)^2 × 100 = 1 W). The total power for all four is 4 W, since P_total = V × I = 40 V × 0.1 A = 4 W.

In a series circuit, the same current flows through every resistor and the total resistance is the sum of the individual resistances. Four 100-ohm resistors give 400 ohms, so the current from a 40 V source is 40/400 = 0.1 A. This current is the same through each resistor, so each one drops 10 V (I × R = 0.1 A × 100 Ω = 10 V). The power in one resistor is P = V × I = 10 V × 0.1 A = 1 W (also P = I^2R = (0.1)^2 × 100 = 1 W). The total power for all four is 4 W, since P_total = V × I = 40 V × 0.1 A = 4 W.