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Fig. III.8 (a) Ac circuit with pure capacitance. (b) Plot of the voltage across the capacitor vc, and the current ic through it. The plot shows a 90° displacement between the current and the voltage.

where / is the frequency in hertz and C is the capacity in farads.

### III.3.4 Summary

Circuit elements are resistance that consumes real power and two reactive elements that only store and give up energy. These two reactive elements, capacitors and inductors, have opposite effects on the phase displacement between the current and voltage in ac circuits. These opposite effects are the key to adding capacitors in an otherwise inductive circuit for purposes of reducing the current-voltage phase displacement. Reducing the phase displacement improves the power factor of the circuit. (Power factor is defined and discussed later.)

tention will be given to the notation used to describe such circuits since vector algebra must be used exclusively.

III.4.1 Circuits with Resistance and Inductive Reactance

Figure III.9 shows a circuit that has both resistive and inductive elements. Such a circuit might represent a real inductor with the resistance representing the wire resistance, or such a circuit might be a simple model of a motor, with the inductance reflecting the inductive characteristics of the motor's windings and the resistance representing both the wire resistance and the real power consumed and converted to mechanical work performed by the motor.

In Figure III.9 the current is common to both circuit elements. Recall that the voltage across the resistor is in phase with this current while the voltage across the inductor leads the current. This idea is shown by plotting these quantities in the complex plane. Since i is the reference, it is plotted on the positive real axis as shown in Figure III.10.

The voltage across the resistor is in phase with the current, so it is also on the positive real axis. whereas the voltage across the inductor is on the positive j axis

Fig. III.9 Circuit with both resistance and inductance. The circuit current i is common to both elements.

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