**Voltage and Current in Series Resonant Circuit:**

The variation of impedance and current with frequency of Voltage and Current in Series Resonant Circuit is shown in Fig. 8.7.

At resonant frequency, the capacitive reactance is equal to inductive reactance, and hence the impedance is minimum. Because of minimum impedance, maximum current flows through the circuit. The current variation with frequency is plotted.

The voltage drop across resistance, inductance and capacitance also varies with frequency. At *f* = 0, the capacitor acts as an open circuit and blocks current. The complete source voltage appears across the capacitor. As the frequency increases, X_{C} decreases and X_{L} increases, causing total reactance X_{C} — X_{L} to decrease. As a result, the impedance decreases and the current increases. As the current increases, V_{R} also increases, and both V_{C} and V_{L} increase.

When the frequency reaches its resonant value *f*_{r}, the impedance is equal to R, and hence, the current reaches its maximum value, and V_{R} is at its maximum value.

As the frequency is increased above resonance, X_{L} continues to increase and X_{C} continues to decrease, causing the total reactance, X_{L}—X_{C} to increase. As a result there is an increase in impedance and a decrease in current. As the current decreases, V_{R} also decreases, and both V_{C} and V_{L} decrease. As the frequency becomes very high, the current approaches zero, both V_{R} and V_{C} approach zero, and V_{L} approaches V_{S}.

The response of different voltages with frequency is shown in Fig. 8.8.

The drop across the resistance reaches its maximum when *f* = *f*_{r}. The maximum voltage across the capacitor occurs at *f* = *f*_{c}. Similarly, the maximum voltage across the inductor occurs at *f* = *f*_{L}.

The voltage drop across the inductor is

where

To obtain the condition for maximum voltage across the inductor, we have to take the derivative of the above equation with respect to frequency, and make it equal to zero.

If we solve for ω, we obtain the value of ω when V_{L} is maximum.

From this

Similarly, the voltage across the capacitor is

To get maximum value dV_{c}/dω = 0

If we solve for ω, we obtain the value of ω when V_{C} is maximum.

From this

The maximum voltage across the capacitor occurs below the resonant frequency; and the maximum voltage across the inductor occurs above the resonant frequency.