An a.c. source of rms voltage and frequency is connected to a series circuit having…

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

Problem

An a.c. source of rms voltage

200\,\text{V}

and frequency

50\,\text{Hz}

is connected to a series circuit having resistance

R = 40\,\Omega

, inductance

L = 0.20\,\text{H}

and capacitance

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

. (i) Calculate the inductive reactance

X_L

and the capacitive reactance

X_C

at this frequency. (ii) Determine the rms current

I

in the circuit and the magnitudes of

V_R

V_L

and

V_C

. (iii) On a sheet of paper draw a scale phasor diagram taking

1\,\text{cm} = 50\,\text{V}

to represent

V_R

V_L

V_C

and the supply voltage

V

. Clearly mark the phase angle

\phi

between

V

and

I

. (iv) From your diagram or otherwise find the numerical value of

\phi

(take the acute angle) and state whether the current leads or lags the supply voltage.