A resistor in an alternating current (AC) circuit serves to limit the flow of current and reduce the voltage.

Resistors are passive components that impede the flow of current within a circuit. In an AC circuit, both the voltage and current continuously change in direction and magnitude. The primary function of a resistor is to restrict the current flow and lower the voltage by converting electrical energy into heat energy. This phenomenon is encapsulated in Ohm’s Law, which states that the current $I$ through a conductor between two points is directly proportional to the voltage $V$ across those points and inversely proportional to the resistance $R$ between them. Mathematically, this is expressed as:

In the context of an AC circuit, the resistor also influences the phase relationship between the voltage and current. The phase angle $\phi$ between the voltage and current is determined by the impedance $Z$ of the circuit, which is a combination of resistance $R$, capacitance $C$, and inductance $L$. While a resistor contributes solely to the resistance component of the impedance, it can still affect the overall phase angle. When a resistor is placed in series with a capacitor or inductor, it can induce a phase shift between the voltage and current.

In summary, the role of a resistor in an AC circuit is to limit the current flow and reduce the voltage, while also contributing to the circuit’s impedance and phase relationship. Resistors are frequently utilized in AC circuits for applications such as voltage dividers, current limiting, and signal conditioning.