(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 ?
(c ) When and inductor is connected to a 200 V DC voltage, a current of 1Aflows trough 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.

Explanation

### Solution

**(a) Expression for Impedance in a Series LCR Circuit:**

1. **Understanding the Components:**
- In a series LCR circuit, we have an inductor (L), a capacitor (C), and a resistor (R) connected in series with an AC source of variable frequency (f).

2. **Impedance Definition:**
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