The instantaneous power in a passive resistor is:

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Multiple Choice

The instantaneous power in a passive resistor is:

Explanation:
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.

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