The instantaneous current in a series circuit is given by

PHYSICS · Subjective · CBSE · Physics · Alternating Current · Alternating Current

Problem

The instantaneous current in a series

RLC

circuit is given by

i(t) = I_0\sin \omega t

. At a certain angular frequency

\omega

the circuit parameters are such that

X_L = 150\,\Omega

and

X_C = 50\,\Omega

while the resistance is

100\,\Omega

. (i) Write expressions (in terms of

I_0

\omega

and

t

) for the instantaneous voltages

v_R(t)

v_L(t)

and

v_C(t)

across each element. (ii) Using a properly labelled qualitative phasor diagram, indicate the relative orientations of

V_R

V_L

V_C

and the supply voltage

V

with respect to the current

I

. (iii) Calculate the phase angle

\phi

between

V

and

I

and state whether the circuit is overall inductive or capacitive at this frequency. (iv) Estimate the time difference (in microseconds) between the peaks of the current and the supply voltage when the applied frequency is

1.0\,\text{kHz}

Related theory

AC Fundamentals
AC Circuit Analysis
Series LCR circuit
AC applied to a series LCR circuit
Alternating Current

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