Series Circuit (With Diagram) | Current | Electrical Engineering

A. C. circuits have three parameters, namely resistance, inductance and capacitance. When all the three parameters are joined in series, the circuit is said to be a general series circuit. Such a circuit is shown in fig. 33 (a) As an inductive coil has both resistance and induc­tance (assumed to be in series), for a general series circuit only two devices are to be joined in series—an inductive coil and a capacitor.

Let an inductive coil of resistance R ohm and inductance L henry be connected in series with a capacitor of capacitance C farad.

Let,  

I = r.m.s. value of current flowing through the circuit,

V_R = r.m.s. voltage across resistance

= IR in phase with I,

V_L = r.m.s. voltage across inductance

= IX_L leading I by 90°,

V_coil = r.m.s. voltage across the inductive coil and is the vector sum of V_R and V_L,

V_C = r.m.s. voltage across the capacitor

= IX_C lagging I by 90°, and

V = r.m.s. voltage applied across the whole circuit and is the vector sum of V_R, V_L and V_C.

Two different vector diagrams of the circuit are shown in fig. 33(b) and 33(c). When the inductive reactance is grater than capacitive reactance (i.e. X_L> X_C or V_L> V_C), the current lags behind the applied voltage by an angle θ, such that,  

This is shown in fig. 33(b). X_L – X_C is called the resultant reactance of the circuit. It is usually denoted by X. Since the current lags behind the applied voltage, the phase angle 0 is called a lagging angle and the power factor cos θ is called a lagging power factor. Thus, the circuit as a whole behaves as an inductive circuit, although inductive influence is reduced by capacitive influence.

Fig. 33(c) shows the vector diagram when capacitive reactance is greater than inductive reactance (i.e. X_C > X_L or V_C > V_L).

Here the current leads the applied voltage by an angle θ, such that,  

The resultant reactance X of the circuit in this case is equal to X_C – X_L, the phase angle θ is a leading angle and the power factor cos θ is a leading power factor. Thus, the circuit as a whole behaves as a circuit containing resistance and capacitance in series, although capacitive influence is reduced by inductive influence.

 

Power absorbed by the circuit:

Both inductance and Capacitance do not absorb any power. Hence, the average power absorbed by the whole circuit is equal to the average power absorbed by the resistance alone and may be given by,  

P = V_RI = I²R watt.

Again, from the vector diagrams,  

V_R = V cos θ volt.

.^.. p = VI cos θ watt.

cos θ is the power factor of the circuit. It may be either lagging or leading,

cos θ = V_R/V = IR/IZ = R/Z