Motor Calculations part4

Problem-As shown in Fig. 6, a resistance of 130 ohms and a capacitance of 30 microfarads are connected in parallel across a 230-volt; 50 hertz supply. Find the following:

(a) Current in each circuit.

(b) Total current.

(c) Phase difference between the total current and the applied voltage.

Fig.-6.-Resistance-and-capacitance-i

(d) Power consumed.

(e) Power factor.

Solution-The capacitive reactance of the circuit is

Motor-Calculations36_thumb_thumb_thu

(a) Current through the resistance is

Motor-Calculations37_thumb_thumb_thu

Current through the capacitance is

Motor-Calculations38_thumb_thumb_thu

(b) Total current is

Motor-Calculations39_thumb3_thumb_th

(c) Phase difference is

Motor-Calculations40_thumb_thumb_thu

(d) Power consumed is

Motor-Calculations41_thumb_thumb_thu

(e) Power factor according to (c) is 0.632, or 63.2%. Problem-Two circuits, Fig. 7, are connected inparallel as shown.

If the voltage of the source is 120, calculate the

(a) Phase displacement.

(b) Power factor of the circuit.

(c) Total current.

Motor-Calculations42_thumb1_thumb_th

Solution-With reference to the vector diagram in Fig. 7, the current through the ohmic resistance is Motor-Calculations43_thumb_thumb_thu

Current through the inductive reactance is

Motor-Calculations44_thumb_thumb_thu

(a) Phase displacement is

Motor-Calculations45_thumb_thumb_thu

(b) Power factor is

Motor-Calculations46_thumb_thumb_thu

(c) Total current is

Motor-Calculations47_thumb_thumb_thu

Problem-Given two circuits (Fig. 8) in parallel, one branch con­ sisting of a resistance of 15 ohms and the other of an inductive reactance of 10 ohms. When the impressed voltage is 110, .find the

(a) Current through the ohmic resistance.

(b) Current through the inductive reactance.

(c) Line current.

(d) Power factor.

(e) Angle of lag of the line current.

Solution-With reference to the vector diagram in Fig. 8, the

Fig.-8.-Resistance-and-inductance-in[2]

(a) Current through the ohmic resistance is

Motor-Calculations48_thumb_thumb_thu

(b) Current through the inductive reactance is

Motor-Calculations49_thumb_thumb_thu

(c) Total line current (IT) is

Motor-Calculations50_thumb_thumb_thu

(d) Power factor is

Motor-Calculations51_thumb_thumb_thu

(e) Angle of lag of the line current is

Motor-Calculations52_thumb_thumb_thu

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