Question

(a) A series circuit having resistance, inductance and capacitance is to be operated on a constant voltage supply of available frequency. Indicate graphically how change takes place in the current and voltage in resistance, inductance and capacitance, and also capacitive reactance and inductive reactance (6)

(b) A resistance of 130Ω and a capacitor of 30µF are connected in parallel across a 230Volt, 50Hz supply. Find the current in each component, total current, phase angle and the power consumed (10)

Answer 1

Consider a R, L, C series circuit as shown.

$$V\:is\:the\:applied\:constant\:voltage$$

$$I\:is\:the\:current\:flowing\:through\:the\:circuit$$

$$X_{L}=inductive\:reactance$$

$$X_{C}=Capacitive\:reactance$$

$$I=\frac{V}{Z}=\frac{V}{\sqrt{R^2+\left(X_{L}-X_{c}\right)^2}}$$

$$Power\:factor\:=\:\cos\phi=\frac{R}{Z}=\frac{R}{\sqrt{R^2}+\left(X_{L}-X_{C}\right)^2}$$

Case (i):

$$R=0;\:X_{C}>X_{L}$$

$$then\:I\:leads\:V\:by\:90^{o}$$

Case (ii):

$$R=0;\:X_{L}>X_{C}$$

$$then\:V\:leads\:I\:by\:90^{o}$$

For Case (i) and (ii):

Case (iii):

$$R\:not\:equal\:to\:zero;\:X_{L}>X_{C}$$

$$then\:I\:lags\:V\:by\:0\:to\:90^{o}$$

Case (iv):

$$R\:not\:equal\:to\:zero;\:X_{C}=X_{L}$$

$$then\:I\:leads\:V\:by\:o\:to\:90^{o}$$

Case (v):

$$R\:not\:equal\:to\:zero;\:X_{L}=X_{C}$$

$$then\:Z=R$$

$$I\:is\:maximum\:and\:in\:phase\:with\:V$$

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