Question

In an LCR series circuit, the value of only capacitance C is varied. The resulting variation of resonance frequency f₀ as a function of C can be represented as

• A.
• B.
• C.
• D.

Answer 1

The Correct Option is C

In an LCR series circuit, the resonance frequency is given by: \[ f_0 = \frac{1}{2\pi \sqrt{LC}} \] From this formula, we see that the resonance frequency \(f_0\) is inversely proportional to the square root of the capacitance \(C\). That means as \(C\) increases, \(f_0\) decreases in a non-linear fashion (specifically, it decreases as a square root function). So the graph of \(f_0\) versus \(C\) will be a decreasing curve, matching option (3) – Option C.

Answer 2

In an LCR circuit, the resonance frequency \( f_0 \) is given by the formula: \[ f_0 = \frac{1}{2\pi \sqrt{LC}} \] where:
\( L \) is the inductance,
\( C \) is the capacitance.
When the capacitance \( C \) is increased, the resonance frequency \( f_0 \) decreases, as shown in the formula.
This implies that \( f_0 \) is inversely proportional to the square root of \( C \).

Therefore, as \( C \) increases, the resonance frequency \( f_0 \) decreases in a curved manner, which corresponds to option (C). Thus, the correct representation of the variation of \( f_0 \) with \( C \) is a decreasing curve.