Motor Calculations part5

Problem-As shown in Fig. 9, a resistance of 10 ohms, an induc tance of 0.06 henry, and a capacitance of 300 microfarads are connected in parallel across a 100-volt, 25-hertz supply. Find the

(a) Current in each circuit.

(b) Total current.

(c) Power factor.

(d) Power consumption.

Solution-In this example, it is first necessary to find the inductive and capacitive reactances. They are, respectively:

(a) Current through the resistance is

Current through the inductive reactance is

Current through the capacitive reactance is

(b) Total current is

(d) Power consumption is

Problem-A circuit connected as shown in Fig. 10 contains a 10-ohm resistance and 0.5-henry inductance in parallel with a capaci tor of 20 microfarads. The voltage and frequency of the source are 1000 and 60, respectively. Find the

(a) Current through the coil.

(b) Phase angle between the current through the coil and the potential across it.

(c) Current through the capacitor.

(d) Total current.

Solution-

(a) The current through the coil is

(b) Phase angle is

With reference to the vector diagram

As the current, I, is the resultant of these two vectors, it is now possible to construct the parallelogram as indicated by the dotted lines. It follows from the construction that {3 OBC = 90°, and from the law of cosines

Problem-A series circuit consists of a 30-microfarad capacitance and a resistance of 50 ohms connected across a 110-volt, 60-hertz supply. Calculate the

(a) lmpedence of the circuit.

(b) Current in the circuit.

(() Voltage drop across the resistance.

(d) Voltage drop across the capacitance.

(e) Angle between the voltage and the current.

(f) Power loss.

(g) Power factor of the circuit.

Solution-

(a) Impedance of the circuit is