A 1.5 -k Ωresistor is connected to an AC voltage source with...

A 1.5 $-k \Omega$ resistor is connected to an AC voltage source with an rms voltage of 120 V. (a) What is the maximum voltage across the resistor? (b) What is the maximum current through the resistor? (c) What is the rms current through the resistor? (d) What is the average power dissipated by the resistor?

Key Concepts

AC Current

In AC circuits, current, like voltage, oscillates over time. The current can be characterized by its maximum (peak) value and its effective (RMS) value, with the RMS value indicating the equivalent steady current that would produce the same heating effect in a resistor.

Ohm's Law

Ohm's law is a fundamental relationship in electrical circuits that relates the voltage across a resistor to the current passing through it via the resistor's resistance. This law, expressed as V = IR, applies in both DC and AC circuits for resistive components.

Average Power

The average power in an AC circuit is the time-averaged rate at which energy is dissipated, typically calculated using the RMS values of voltage or current. For a resistor, the power can be determined using formulas such as P = V_RMS^2/R or P = I_RMS^2 * R, reflecting how the effective values contribute to energy dissipation over time.

RMS Voltage

In alternating current (AC) circuits, the RMS (root-mean-square) voltage is a measure of the effective voltage that produces the same power dissipation in a resistor as an equivalent direct current (DC) voltage. It is calculated by taking the square root of the mean of the squared instantaneous values over one cycle.

Peak Voltage

The peak voltage of an AC waveform is the maximum instantaneous value reached by the voltage during each cycle. For sinusoidal waveforms, it is mathematically related to the RMS voltage by a constant factor, reflecting the geometry of the sine wave.

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