Single-Phase a.c. Calculations

Abstract

A single-phase circuit containing a resistor, an inductor and a capacitor is shown in Figure 12.1. You will recall that the phase relationship between the voltage and the current in a circuit element depends on the nature of the element, in other words, is it an R or an L or a C? This means that in an a.c. circuit you cannot simply add the numerical values of V _R , V _L and V _C together to get the value of the supply voltage V _S ; the reason for this is that the voltage phasors representing V _R , V _L and V _C ‘point’ in different directions relative to the current on the phasor diagram. To account for the differing ‘directions’ of the phasors, you have to calculate V _S as the phasor sum of the three component voltages in Figure 12.1. That is

$${\rm{supply voltage, }}{V_S} = {\rm{ }}{\bf{phasor sum}}{\rm{ of }}{V_R},{V_L}{\rm{ and }}{V_C}$$

To illustrate how this is applied to the circuit in Figure 12.1, consider the case where the current, I, is 1.5 A, and the three voltages are

$${V_R} = 150{\rm{V, }}{V_L} = 200{\rm{V, }}{V_C} = 100{\rm{V, }}$$

We shall consider in turn the phasor diagram for each element, after which we shall combine them to form the phasor diagram for the complete circuit.