An inductor 20 mH, a capacitor 100 μF and a resistor 50 Ω are connected in series across a source of emf, V = 10 sin 314 t. The power loss in the circuit is

CONCEPT:

The power loss in the circuit is equal to the product of the square of current and resistance and written as;

P_av = I²R

Here, 'I' is the current.

 ----(1)

P_av is the power loss, V_RMS is the root mean square potential, Z is the impedance and R is the resistance in the circuit.

and impedance in the LCR is written as;

 ---(2)

Here, X_L is the inductive reactance and X_C is the Capacitive reactance.

CALCULATION:

By using equation (2) the impedance is written as,

The inductive reactance is equal to  and capacitive reactance is equal to . Where  is the resonant frequency, L is inductance and C is capacitance.

On putting the values of  inductive reactance and capacitive reactance we get;

 -----(3)

Given:

L = 20 mH = 20  10^-3 H

C = 100 μF = 

R =  50 Ω

V_RMS = 10 V

and,  = 314 Hz

Now, Putting these values in equation (3) we have,

⇒ Z = 

Now, on putting the value of Z in equation (1) we get;

⇒ P_av = 0.79W

Hence, option 1) is the correct answer.