MHT CET · Physics · Alternating Current
A \(10 \Omega\) resistance, \(5 \mathrm{mH}\) coil and \(10 \mu \mathrm{F}\) capacitor are joined in series. When alternating current source of suitable frequency is joined to this combination, the circuit resonates. If the resistance is halved, the resonant frequency is
- A quadrupled.
- B halved.
- C doubled.
- D remains unchanged.
Answer & Solution
Correct Answer
(D) remains unchanged.
Step-by-step Solution
Detailed explanation
Concept based.
At resonance, in LCR circuit inductive and capacitive reactance are equal:
\(\begin{aligned}
& X_L=X_C \\
& \Rightarrow 2 \pi \mathrm{fL}=\frac{1}{2 \pi \mathrm{fC}} \\
& \Rightarrow \mathrm{f}^2=\left(\frac{1}{4 \pi^2 \mathrm{LC}}\right)
\end{aligned}\)
The resonant frequency is independent of the resistance.
At resonance, in LCR circuit inductive and capacitive reactance are equal:
\(\begin{aligned}
& X_L=X_C \\
& \Rightarrow 2 \pi \mathrm{fL}=\frac{1}{2 \pi \mathrm{fC}} \\
& \Rightarrow \mathrm{f}^2=\left(\frac{1}{4 \pi^2 \mathrm{LC}}\right)
\end{aligned}\)
The resonant frequency is independent of the resistance.
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