12.5 VIBRATION OF CURRENT AND VOLTAGES WITH
FREQUENCY IN A SERIES RLC CIRCUIT

In a series RLC circuit, impedance Z is given by

Hence, current I in the series circuit is given by

Magnitude

At resonance, and Z = R and this is the minimum value of Z.
Hence, from Equation (12.8), at resonance,

Hence, the current is maximum at resonance, therefore this type of
circuit is known as an acceptor circuit.

At frequencies either below or above the resonance frequency, Z is
greater than R so that I is smaller than The curve marked I in Figure 12.8
shows the nature of variation of current I with frequency.

The voltage across the capacitor C is given by

Hence, magnitude

The curve marked V_C in Figure 12.8 gives the variation of voltage V_C with
frequency.

The frequency f_C at which V_C is maximum may be obtained by equating
to zero. This results in

Obviously f_C < f_r .

The voltage across the inductor L is given by

The magnitude

The curve marked V_L in Figure 12.8 gives the variation of V_L with frequency.
The frequency f_L at which V_L is maximum may be obtained by equating
to zero. Thus, we get

Obviously, f_L > f_r .

It may be seen from Equation (12.15) that f_L > f_r .

Voltages V_C and V_l have equal values and opposite phases at the frequency
of resonance f_r as shown by their point of intersection P.

If R is extremely small, both f_L and f_C tend to equal f_r.

FIGURE 12.8   Variation of I_C, V_C, and V_l with frequency in a series RLC circuit.

Example 12.7.  A series RLC circuit consists of resistance R = 20Ω, inductance
L = 0.01H, and capacitance C = 0.04μF. Calculate the frequency of
resonance. If a 10 volts voltage of frequency equal to the frequency of resonance
is applied to this circuit, calculate the values of voltages V_C and V_L
across C and L, respectively. Find the frequencies at which these voltages V_C
and V_L are maximum.

Solution:

At

Hence,

The frequency at which V_C is maximum is given by

The frequency at which V_l is maximum is given by