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: Think about the limits:
For $f \to 0$, the capacitor blocks the current, so $i \to 0$. For $f \to \infty$, the inductor blocks it, so $i \to 0$.

Step 2: In between:
There must be a frequency $f_0 = \frac{1}{2\pi\sqrt{LC}}$ where the two reactances cancel and the current is largest. The graph is therefore a single-peaked bell curve.

Step 3: Match:
Graph (P) is the smooth bell. Graphs (Q) and (S) have a dip, and (R) has a kink-like spike.

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