A lamp has power 4 W and a resistance of 16 Ω. What is the current when operated at its rated voltage?

A lamp has power 4 W and a resistance of 16 Ω. What is the current when operated at its rated voltage?

• A. 1 A
• B. 0.5 A
• C. 4 A
• D. 2 A

Answer: (B)

Current through a resistor is determined by the relation P = I^2 R. With a power of 4 W and a resistance of 16 Ω, the current is I = sqrt(P/R) = sqrt(4/16) = sqrt(0.25) = 0.5 A. Another way to see it is to find the rated voltage first: V = sqrt(P R) = sqrt(4×16) = 8 V, and then I = V/R = 8/16 = 0.5 A. If the current were 1 A, the power would be 1^2 × 16 = 16 W; with 2 A or 4 A, the power would be 64 W or 256 W, respectively, which doesn’t match the given 4 W. So the current at the rated voltage is 0.5 A.

Current through a resistor is determined by the relation P = I^2 R. With a power of 4 W and a resistance of 16 Ω, the current is I = sqrt(P/R) = sqrt(4/16) = sqrt(0.25) = 0.5 A. Another way to see it is to find the rated voltage first: V = sqrt(P R) = sqrt(4×16) = 8 V, and then I = V/R = 8/16 = 0.5 A. If the current were 1 A, the power would be 1^2 × 16 = 16 W; with 2 A or 4 A, the power would be 64 W or 256 W, respectively, which doesn’t match the given 4 W. So the current at the rated voltage is 0.5 A.