In a series LCR circuit connected to an ac source of variable frequency and voltage `v =v_(m) sin omega t, ` draw a plot showing the variation of current (I) with angular frequency `(omega)` for two different values of resistance `R_(1) and R_(2) (R_(1) gt R_(2))`. Write the condition under which the phenomenon of resonance occurs. For which value of the resistance out of the two curves, a sharper resonance is produced ? Define Q-factor of the circuit and give its significance.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understanding the LCR Circuit
An LCR circuit consists of an inductor (L), a capacitor (C), and a resistor (R) connected in series. When connected to an AC source with voltage \( v = V_m \sin(\omega t) \), the circuit's behavior depends on the frequency of the source.

### Step 2: Impedance in the LCR Circuit
The impedance \( Z \) of the circuit can be expressed as:
\[
...