(a) A 1.7-H inductor is connected across 230-V rms, 50-Hz...

(a) A 1.7-H inductor is connected across 230-V rms, 50-Hz power. Find the rms inductor current. (b) Repeat if the same inductor is connected across the $120-\mathrm{V} \mathrm{ms}, 60-\mathrm{Hz}$ power commonly used in North America.

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Key Concepts

Root Mean Square (RMS) Values

RMS values are used to measure the effective or equivalent DC value of an alternating current or voltage, allowing for meaningful comparisons and power calculations in AC circuits. The RMS value gives the constant voltage or current that would deliver the same power to a resistor as the AC waveform does.

AC Circuit Impedance

In AC circuits, impedance extends the concept of resistance to account for the phase shift between voltage and current caused by reactive components like inductors. For a pure inductor, the impedance is purely imaginary and equal to jX_L, where X_L is the inductive reactance, thereby determining the amplitude and phase of the current in response to an applied AC voltage.

Inductive Reactance

Inductive reactance is the opposition that an inductor provides to alternating current due to its tendency to resist changes in current. It is calculated using the formula X_L = 2?fL, where f is the frequency and L is the inductance. This reactance determines how much the inductor will resist the AC voltage applied across it, thereby affecting the resulting current.

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