Example 28.2: A radio transmitter applies 480 V rms across a 6800-pF capacitor and an inductor,

step 1 In this problem, we are given the RMS voltage of 480 volts, a capacitance of 6 ,800 picofarad, a

Example 28.2: A radio transmitter applies 480 V rms across...

Example 28.2: A radio transmitter applies $480 \mathrm{~V}$ rms across a $6800-\mathrm{pF}$ capacitor and an inductor, connected in parallel to make a resonant circuit that determines the transmitter's frequency. The resulting current in each component is $22.0 \mathrm{~A} \mathrm{rms}$. Find (a) the transmitter frequency and (b) the inductance.

Key Concepts

RMS Values in AC Circuits

Root Mean Square (RMS) values represent the effective or equivalent DC values of AC voltages and currents, which are essential for computing power. RMS values allow engineers to analyze AC circuits by treating them similarly to DC circuits, simplifying the calculation of power dissipation and ensuring that the alternating quantities are compared accurately with their DC counterparts.

Capacitive and Inductive Reactance

Capacitive reactance (Xc) and inductive reactance (Xl) describe the opposition that capacitors and inductors provide to alternating current. Capacitive reactance is defined as Xc = 1/(?C) and decreases with increasing frequency, while inductive reactance is defined as Xl = ?L and increases with frequency. Their frequency-dependent behavior is critical in analyzing and designing AC circuits, especially those involving resonance.

Resonant Frequency in LC Circuits

Resonant frequency is the frequency at which the inductive and capacitive reactances in an LC circuit are equal in magnitude but opposite in phase, which causes them to cancel each other. This condition leads the circuit to behave as if it were resistive, and the resonant angular frequency is given by ? = 1/?(LC). Knowing this relationship allows one to determine the circuit’s frequency or one of the component values when the other parameters are known.

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