A 50.0Ωresistor is connected as in Fig. 31-8 to an ac...

A 50.0$\Omega$ resistor is connected as in Fig. $31-8$ to an ac generator with $8_{m}=30.0 \mathrm{V}$ . What is the amplitude of the resulting alternating current if the frequency of the emf is (a) 1.00 $\mathrm{kHz}$ and (b) 8.00 $\mathrm{kHz}$ ?

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Key Concepts

Ohm’s Law in AC Circuits

Ohm’s law relates the voltage across a circuit element to the current through it, even in alternating current (AC) circuits. In the context of AC, the amplitude of the current is given by dividing the amplitude of the voltage by the impedance of the circuit, providing a foundation for understanding how AC sources drive currents through various circuit elements.

Impedance

Impedance is a fundamental concept in AC circuits that extends the idea of resistance to include the effects of reactance from capacitors and inductors. It is a complex quantity that determines how much a circuit resists the flow of AC, and in purely resistive circuits, the impedance is simply equal to the resistance, making the current amplitude independent of frequency.

Frequency Dependence in AC Circuits

Frequency plays a crucial role in AC circuit behavior when reactive components like capacitors and inductors are present, as their reactance varies with the frequency of the AC source. However, in circuits that are purely resistive, the impedance remains constant regardless of frequency, which means the amplitude of the current is solely determined by the voltage amplitude and the resistive value.

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