CBSE Class 12-science Answered

When the element X is connected across an a.c. source of a given voltage, the current is in phase with the applied voltage. This implies that the circuit element X is a resistance R.

When the circuit element Y is connected in series with X across an a.c. source, the voltage is found to lead the current by a phase angle p/4. This indicates that the circuit element Y is an inductance L.

The circuit element Z is a capacitance C as it is found that the current leads the voltage by a phase angle p/4.

When the three circuit elements—resistance, inductance and capacitance—are connected in series with the a.c. source, the impedance of the circuit is given by

where R is the resistance, X_L is the inductive reactance and X_C is the capacitive reactance.

The variation of current with the changing frequency of applied voltage in a circuit in which X, Y and Z are connected in series is as shown below:

Such an LCR circuit connected in series admits maximum current corresponding to a given frequency of a.c. This frequency is known as series resonance frequency.

At resonant frequency w₀, the impedance of the LCR circuit is minimum, and hence, the current becomes maximum.

For frequencies greater than or less than w₀, the values of current are less than the maximum current value I₀. As a series resonance circuit admits maximum peak current through it at resonance, it is called an acceptor circuit. Such circuits find application in radios, TV receiver sets etc.