Category: Single-phase AC Circuits

A circuit that contains a pure resistance R Ω connected in series with a pure capacitor of capacitance C Farad is known as R–C series circuit. An R–C series circuit and its phasor diagram is shown in Figures 7.21 and 7.22, respectively. To draw the phasor diagram, current I (rms value) is taken as the reference vector. Voltage drop in resistance VR (=IR) is taken in phase…

In AC circuits, the power factor may be expressed as pf = cos ɸ = R/Z = true power/apparent power In the case of pure resistive circuit, current is in phase with circuit voltage, that is, ɸ = 0. Therefore, power factor of the circuit, cos ɸ = 1. While in the case of pure inductive or capacitive circuit, current is 90° out…

The power that is actually consumed or utilised in an AC circuit is called true power or active power or real power. It has already been seen that power is consumed only in resistance. A pure inductor and a pure capacitor do not consume any power, since in a half cycle whatever power is received…

The simplified phasor diagram of R–L series circuit is shown in Figure 7.10. When each side of this phasor diagram is divided by a common factor I, we get another right−angled triangle, as shown in Figure 7.11, whose sides represent R, XL, and Z. Such a triangle is known as impedance triangle. Fig. 7.10  Phasor diagram for R−L series circuit Therefore, a…

A circuit that contains a pure resistance R Ω connected in series with a coil having pure inductance of L Henry is known as R–L series circuit. This is the most general case that we come across in practice. Fig. 7.7  Circuit containing resistance and inductance in series An R–L series circuit and its phasor diagram are shown in Figures 7.7 and 7.8,…

So far, we have dealt with simple AC circuits containing pure components such as resistance, inductance, and capacitance. However, in actual practice, AC circuits contain two or more than two such components connected in series or parallel. A series circuit is a circuit in which each component carries the same current. An AC series circuit…

The circuit containing a pure capacitor of capacitance C Farad is shown in Figure 7.5. Let the alternating voltage applied across the circuit be given as Fig. 7.5  Circuit diagram containing pure capacitor only ν = Vm sin ω t        (7.6) Charge on the capacitor at any instant,   q = Cv Current flowing through the circuit, or or where XC = 1/ω C is the opposition offered to the flow…

The circuit containing a pure inductance of L Henry is shown in Figure 7.3. Fig. 7.3  Circuit containing pure inductance only Let the alternating voltage applied across the circuit be given by the equation;   ν = Vm sin ω t        (7.4) As a result, an AC i flows through the inductance that induces an emf in it, given by the relation; This induced emf is equal…

The circuit containing a pure resistance of R Ω is shown in Figure 7.1. Let the alternating voltage applied across the circuit be given by the equation; Fig. 7.1  Circuit containing resistance only ν = Vm sin ω t        (7.1) Then, the instantaneous value of current flowing through the resistor will be; The value of current will be maximum when   ω t = 90°   or   sin ω t = 1 Im = Vm/R…

Alternating supply is invariably used for domestic and industrial applications. The path for the flow of alternating current is called an AC circuit. In DC circuits, the opposition to the flow of current is only the resistance of the circuit. While in AC circuits, the opposition to the flow of current is due to resistance (R),…