Question

Which graph shows the correct variation of r.m.s. current '\(i\)' with frequency '\(f\)' of a.c. in case of series resonant circuit ?

• A. \((R)\)
• B. \((P)\)
• C. \((S)\)
• D. \((Q)\)

Hint:

Current rises to a maximum at resonance and falls on both sides, so the graph is a smooth peak.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
In a series LCR circuit the impedance is \(Z = \sqrt{R^2 + (X_L - X_C)^2}\). It is smallest, equal to \(R\), at the resonant frequency where \(X_L = X_C\).

Step 2: Effect on current:
\(i_{rms} = \frac{V}{Z}\). At low frequency \(X_C\) is large, so \(Z\) is large and the current is small. At resonance \(Z\) is minimum, so the current is maximum. At high frequency \(X_L\) is large and the current falls again.

Step 3: Read the graphs:
Graph (P) shows a smooth bell-shaped curve with one maximum in the middle, rising from low values and falling again. This is the required shape.

Step 4: Why the other graphs are wrong.
Graphs (Q) and (S) are valleys, showing a minimum of current, which is the behaviour of a parallel resonant circuit. Graph (R) has a sharp spike on top of straight slopes, which is not the smooth variation of \(\frac{V}{Z}\).

Final Answer:
Graph (P) is correct, option (B). \[ \boxed{\text{(P)}} \]