The instantaneous power in a passive resistor is:

The instantaneous power in a passive resistor is:

• A. V / R
• B. V^2 / R
• C. V * R
• D. R^2 / V

Answer: (B)

Power absorbed by a resistor at any instant is the product of the instantaneous voltage and current: p(t) = v(t) i(t). For a resistor, current relates to voltage by Ohm’s law i = v/R, so p(t) = v(t) [v(t)/R] = v(t)^2 / R. This shows why the expression V^2 / R is the correct way to write instantaneous power for a resistor. Equivalently, p(t) = i(t)^2 R, which leads to the same result when i = v/R. The other forms would not represent power: V/R is the current, V*R has incorrect units, and R^2/V also does not correspond to power.

Power absorbed by a resistor at any instant is the product of the instantaneous voltage and current: p(t) = v(t) i(t). For a resistor, current relates to voltage by Ohm’s law i = v/R, so p(t) = v(t) [v(t)/R] = v(t)^2 / R. This shows why the expression V^2 / R is the correct way to write instantaneous power for a resistor. Equivalently, p(t) = i(t)^2 R, which leads to the same result when i = v/R. The other forms would not represent power: V/R is the current, V*R has incorrect units, and R^2/V also does not correspond to power.