Question

Design an AC RLC circuit that can supply power to a load which is made up of an 8 - mu*F capacitor and a resistor with a resistance that can be varied between 600 Q and 800 The average power consumed by the circuit must be 2 kW or less and the power factor must be above 0.95 for all conditions of the load. The frequency of the power supply is 50 Hz. The design should include an inductor and appropriate sinusoidal voltage source and descriptions of the circuit impedance, phase angle, the current flow and voltage drops across all components. Show all calculations to prove that the design requirements are met. (show explanation and step by step).

Answer 1

For the power factor we just need to choose an inductor in such a way that it meets the requirement,

Given ; cos > 0.95

< cos^-1(0.95)

tan < tan(cos^-1(0.95))

tan < 0.33

Now, assuming X to be the total reactance of the circuit;

|X| < 0.33R

Now for the maximum value of X statisfying this condition always; R = 600

|X| < 0.33 x 600 = 197.21

Also, for voltage supply we use the condition for maximum power to be supplied in circuit;

(V_rms²/Z)cos < 2KW

V_rms²< 2000Z/cos

For the max value of V_rms satisfying this condition Z has to be minimum and cos has to be maximum which is

Z = 600

cos = 1

=> V_rms < 1095.445 V

For the inductor;

X < 197.21

0 < 1/wC - wL < 197.21

=> 0 < 1/w²C - L < 197.21/w

=> 1.27 > L > 0.64

These are the conditions for the inductor, voltage source.

So, lets assume the inductor to be 1H, power supply to be 500V amplitude and phase angle 0.

Now just construct an RLC circuit with these components and you will get your design satisfying all the conditions