A capacitor of capacitance is connected in series with a resistor and an inductor to…

PHYSICS · Multi-part · CBSE · Physics · Alternating Current · Alternating Current

Problem

A capacitor of capacitance

C = 100\,\mu\text{F}

is connected in series with a resistor

R

and an inductor

L

to a

200\,\text{V}

(rms),

50\,\text{Hz}

AC source. The circuit draws an rms current of

4\,\text{A}

and the rms voltage across the resistor is observed to be

120\,\text{V}

. (i) Determine the resistance

R

. (ii) Using the given data, calculate the magnitude of the net reactive voltage in the circuit. (iii) Hence obtain the numerical value of

(X_L - X_C)

and find the inductive reactance

X_L

. (iv) Determine the inductance

L

of the coil. (v) Sketch a labelled phasor diagram showing the supply voltage, the component voltages and the current, and use it to check your numerical answers.

Related theory

Power in AC Circuits
AC Circuit Analysis
Alternating current
Series LCR circuit
AC applied to a series LCR circuit

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