Question

A $20\Omega$ resistance, $10\text{ mH}$ inductance coil and $15\mu\text{F}$ capacitor are joined in series. When a suitable frequency alternating current source is joined to this combination, the circuit resonates. If the resistance is made $\frac{1}{3}\text{rd}$, the resonant frequency}

• A. remains unchanged.
• B. is doubled.
• C. is quadrupled.
• D. is halved.

Hint:

Resistance ($R$) only affects the "sharpness" (Quality Factor) and "peak current" of the resonance, not the "position" (frequency).

Answer 1

The Correct Option is A

Step 1: Concept
The resonant frequency ($f_r$) of a series LCR circuit is given by $f_r = \frac{1}{2\pi\sqrt{LC}}$.

Step 2: Meaning
This frequency is the point where the inductive reactance ($X_L$) equals the capacitive reactance ($X_C$).

Step 3: Analysis
In the formula for resonant frequency, the variables are $L$ (inductance) and $C$ (capacitance). The resistance ($R$) does not appear in the expression for $f_r$.

Step 4: Conclusion
Changing the resistance affects the current at resonance, but the resonant frequency itself remains unchanged. Final Answer: (A)