Answer to Question #86731 in Electric Circuits for Adam

Question

A resistance R and inductance L=0.01 H and a capacitance are connected in series when a voltage V=400Cos (300t-10) v is applied to the series combination, the current flowing I=10 √2cos (300t-55°)A. Find P and C.

Answer 1

The active power:

$$P=\frac{1}{2}VI\text{cos}(\phi_V-\phi_I)=$$ $$=\frac{1}{2}\cdot400\cdot10\sqrt{2}\text{cos}(-10^\circ-(-55^\circ))=2000\text{ W}.$$

Find the resistance:

$$R=\frac{P}{I^2}=\frac{2000}{10^2}=20\space\Omega.$$

Write Ohm's law for the circuit:

$$Z=\sqrt{R^2+(\omega L-1/\omega C)^2}=\frac{V}{I},$$

$$20^2+(300\cdot0.01-\frac{1}{300 C})^2=(\frac{400}{10\sqrt{2}})^2,$$

$$C=144.93\space\mu\text{F}$$