Question

To increase the resonant frequency in series LCR circuit-

• A. Source frequency should be increased
• B. Another resistance should be added in series with the first resistance.
• C. Another capacitor should be added in series with the first capacitor.
• D. The source frequency should be decreased.

Answer 1

The Correct Option is C

To understand how to increase the resonant frequency in a series LCR circuit, let's analyze the situation and the relevant formula.

The resonant frequency \((f_0)\) of a series LCR circuit is given by:

f_0 = \frac{1}{2\pi\sqrt{LC}}

Where:

• L is the inductance of the coil,
• C is the capacitance of the capacitor,
• \(\pi\) is a mathematical constant (approximately 3.14159).

From the formula, it is clear that the resonant frequency depends inversely on the square root of the inductance and the capacitance. To increase the resonant frequency, the value of L or C needs to be decreased.

The given options are:

• Source frequency should be increased.
• Another resistance should be added in series with the first resistance.
• Another capacitor should be added in series with the first capacitor.
• The source frequency should be decreased.

Options 1 and 4 refer to changing the source frequency, which does not affect the circuit's inherent resonant frequency as calculated by the formula.

Option 2 suggests adding another resistance, which does not impact the values of L or C and thus will not change the resonant frequency.

Option 3 suggests adding another capacitor in series with the first capacitor. This effectively changes the total capacitance (C_{\text{total}}) in the circuit. When capacitors are added in series, their total capacitance is reduced, calculated as:

\frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_2} + \ldots

Thus, adding another capacitor in series decreases the total capacitance, C_{\text{total}}, which in turn increases the resonant frequency.

Therefore, the correct option is: Another capacitor should be added in series with the first capacitor.