Physics

Physics

Problem

A 30 Ω30\,\Omega resistor and a 150 mH150\,\text{mH} inductor are connected in series with an unknown capacitor across an a.c. source that delivers a peak voltage of 170 V170\,\text{V} at 50 Hz50\,\text{Hz}. The rms current in the circuit is found to be 0.40 A0.40\,\text{A}. a. (a) Convert the given peak voltage to its rms value. b. (b) Determine the impedance of the circuit from the given data. c. (c) Find the magnitude of the net reactance of the circuit. d. (d) Calculate the value of the capacitance connected in the circuit.
Intuitive explanation

This is an RLC circuit resonance problem where you need to find the capacitance by working backward from the impedance. The key insight is that the rms current tells you the total impedance ZZ, and you can use that to solve for the unknown capacitive reactance—then convert it to capacitance. Remember that inductive and capacitive reactances oppose each other, so they partially cancel in the impedance formula.

Intuitive explanation

This is an RLC circuit resonance problem where you need to find the capacitance by working backward from the impedance. The key insight is that the rms current tells you the total impedance ZZ, and you can use that to solve for the unknown capacitive reactance—then convert it to capacitance. Remember that inductive and capacitive reactances oppose each other, so they partially cancel in the impedance formula.

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