In a laboratory activity a class draws a scale phasor diagram for a certain series circuit

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

Problem

In a laboratory activity a class draws a scale phasor diagram for a certain series

RLC

circuit. The diagram is made with the following scale:

1\,\text{cm} = 20\,\text{V}

. The measured lengths on the diagram are: •

V_R

3.0\,\text{cm}

along the positive

x

–axis, •

V_L

4.5\,\text{cm}

upward along the positive

y

–axis, •

V_C

2.0\,\text{cm}

downward along the negative

y

–axis. The rms current in the circuit, measured independently, is

2.0\,\text{A}

. (i) Using the scale information, calculate the numerical values of

V_R

V_L

and

V_C

. (ii) Determine the resistance

R

, inductive reactance

X_L

and capacitive reactance

X_C

of the circuit. (iii) Hence find the values of

L

and

C

if the supply frequency is

60\,\text{Hz}

. (iv) Using the phasor addition verify Kirchhoff’s voltage law by computing the magnitude of the supply voltage

V

and comparing it with the vector sum of

V_R

V_L

and

V_C

obtained from the scale drawing. (v) Calculate the power factor of the circuit for the given frequency.