Resistance, Inductance and Capacitance in AC Series

The following figure shows resistance, inductance and capacitance connected in an AC series.

FIGURE

        The following is the waveform diagram and the phasor diagram that shows that the voltage across the resistor (V_R) is in-phase with the current, across the inductor (V_L) is 90^o ahead and that across the capacitor (V_C) is 90^o behind.

FIGURE

FIGURE

        The phasor diagram, shows that the total reactive voltage is V_L – V_C. Thus the current lags the voltage making the circuit more inductive.

Impedance: In this case, the opposition to current flow is calculated using the following formula.

Resonance: The frequency varies in case of series circuit consisting of resistor, inductor and capacitor. The frequency rise causes the rise in inductive reactance (X_L) and fall in capacitive reactance (X_C). The resonance occurs at a certain frequency, known as resonant frequency (f₀), which is shown in the graph below.

FIGURE

        If X_L = X_C, then V_L = V_C and Z = R. Therefore, the impedance is at a minimum and the current will be at a maximum. The phasor diagrams are shown below.

FIGURE

        The formula for resonant frequency is given below.

Selectivity: The property of a tuned circuit which enables it to respond to a particular signal and discard others at different but close frequencies is known as the selectivity (Q) and Q factor at resonance is represented as Q₀. The resistance and the ratio of inductance and capacitance are the factors affecting the selectivity of the series circuit. If the resistance is doubled, the current is halved and reduces selectivity. The increase in L/C ratio improves the selectivity of the circuit.

        The bandwidth of the circuit is the range of frequencies over which at least half of the maximum power and current is provided. A narrow bandwidth is required for good selectivity.