An AC source operating at 60 . Hz with a maximum voltage of 170 V is connected in series with a

step 1 In this question, we have this RL circuit. So we are given the values of the voltage, maximum vo

An AC source operating at 60 . Hz with a maximum voltage of...

An AC source operating at $60 . \mathrm{Hz}$ with a maximum voltage of 170 $\mathrm{V}$ is connected in series with a resistor $(R=1.2 \mathrm{k} \Omega)$ and an inductor (L 5 2.8 H). (a) What is the maximum value of the current in the circuit? (b) What are the maximum values of the potential difference across the resistor and the inductor? (c) When the current is at a maximum, what are the magnitudes of the potential differences across the resistor, the inductor, and the AC source? (d) When the current is zero, what are the magnitudes of the potential difference across the resistor, the inductor, and the AC source?

Key Concepts

Phasor Representation

Phasor representation is a technique used to simplify the analysis of AC circuits by converting sinusoidally varying quantities into complex numbers that capture both magnitude and phase. This method allows for easy addition, subtraction, and comparison of sinusoidal functions, making it straightforward to analyze how voltages across resistors and inductors relate to the source voltage, particularly when considering conditions like maximum current or zero crossing.

Kirchhoff’s Voltage Law in AC Circuits

Kirchhoff’s Voltage Law (KVL) states that the algebraic sum of the instantaneous potential differences in any closed loop of a circuit must equal zero, even in AC circuits. This principle is applied to determine how the voltage divides among various components—such as resistors and inductors—in a series circuit, especially when analyzing different instantaneous scenarios like when current is at its maximum or zero.

Inductive Reactance

Inductive reactance is the opposition offered by an inductor to changes in current, and it increases linearly with frequency. Represented as XL = ?L, this term quantifies how the inductor affects the phase and amplitude of current relative to voltage in AC circuits. It directly influences the overall impedance in RL circuits, thereby affecting the circuit’s behavior under varying frequencies.

Impedance in RL Circuits

Impedance is a measure of total opposition to current flow in an AC circuit, combining both resistance and reactance. In a series RL circuit, impedance is calculated using the formula Z = ?(R² + (?L)²), where R is the resistance, ? (omega) is the angular frequency, and L is the inductance. This concept is essential for determining the magnitude of the current given an applied voltage and for understanding how the resistor and inductor share voltage drops.

AC Circuit Analysis

AC circuit analysis involves examining circuits powered by alternating currents, where voltages and currents vary sinusoidally with time. This subject covers calculations with peak values, average values, and RMS (root mean square) values, all of which are crucial for understanding how different components behave under sinusoidal excitation.

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