Effect of changing capacitance on resonant frequency: In a series RLC circuit, what happens to the resonant frequency when the capacitance C is decreased while L remains the same?

Introduction / Context:Designers often adjust capacitance to tune a circuit. Understanding the mathematical relationship between C and resonant frequency f0 prevents trial-and-error and speeds up practical filter and oscillator design.

Given Data / Assumptions:

• Series RLC topology.
• Inductance L constant; capacitance C is reduced.
• Standard resonance definition f0 = 1 / (2π√(LC)).

Concept / Approach:

Because f0 is inversely proportional to √C (for fixed L), decreasing C decreases √C and therefore increases f0. This inverse-square-root dependence is monotonic and predictable.

Step-by-Step Solution:

Verification / Alternative check:

Numerical illustration: If C is reduced by factor of 4, √C halves and f0 doubles—confirming a higher frequency.

Why Other Options Are Wrong:

'Decreases' contradicts the formula. 'Is not affected' is incorrect because f0 explicitly depends on C. 'Is reduced to zero' is physically meaningless here.

Common Pitfalls:

Assuming a linear inverse with C; forgetting the square-root relationship; confusing series and parallel circuits (both share the same f0 expression).

Final Answer:

increases