Question

A 1.11-µH inductor is connected in series with a variable capacitor in the tuning section of a short wave radio set. What capacitance tunes the circuit to the signal from a transmitter broadcasting at 6.55 MHz?

Answer 1

Concepts and reason

The concept used to solve this problem is resonant frequency of the LC circuit.

Initially, the angular frequency can be calculated by using the relation between angular frequency and the linear frequency. Later, the capacitance connected in the circuit can be calculated by using the expression between inductance, capacitance and the angular frequency.

Fundamentals

Resonance occurs when the capacitive and inductive reactance are equal to each other.

The expression for the angular frequency is as follows:

$@=21f $

Here, is the angular frequency and is the linear frequency.

The expression for the resonant frequency of the LC circuit is as follows:

Here, is the capacitance connected in the circuit and is the inductance connected in the circuit.

The expression for the angular frequency is as follows:

$@=21f $

Substitute for.

The expression for the capacitance connected in the circuit is as follows:

Rewrite the expression for the capacitance as follows:

Substitute for and for .

Ans:

Thus, the value of the capacitance connected in the circuit is .