Question

(a)
In a series LCR circuit connected across an ac source of variable frequency,
obtain the expression for its impedance and draw a plot showing its variation
with frequency of the ac source.
(b)
What is the phase difference between the voltages across inductor and the
capacitor at resonance in the LCR circuit ?
(e) When an inductor is connected to a 200 V de voltage, a current of 1A flows
through it. When the same inductor is connected to a 200 V, 50 Hz ac source,
only 0.5 A current flows. Explain, why ? Also, calculate the self inductance of
the inductor.​

Answer 1

Explanation:

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Answer 2

Thus the frequency of the AC supply is 50 Hz.

Explanation:

Question statement:

When a dc voltage of 200 V is applied to a coil of self-inductance (2  √3  /π) H, a current of 1 A flows through it. But by replacing dc source with ac source of 200 V, the current in the coil is reduced to 0.5 A. Then the frequency of ac supply is:

Solution:

Let, R= resistance of coil

When DC connected

R =  I  / V  =  200  / 1​  = 200 Ω

When AC source 200 V is applied, I=  

(200)  / √(200)^2  + ω^ 2  L^2      ........(1)

Given, I = 0.5 A

L=2  √3 / π and e know

ω = 2πf

Putting these values in (1) and solving for f.

f = 50 Hz

Thus the frequency of the AC supply is 50 Hz.