Answer to Question #108875 in Electrical Engineering for Badd

Question

1.

A 400 mH coil of negligible resistance is connected to an AC circuit in which an effective current of 6 mA is flowing. Find out the voltage across the coil if the frequency is 1000 Hz.

2.

A capacitor of capacitance 102/π µF is connected across a 220 V, 50 Hz A.C. mains. Calculate the capacitive reactance, RMS value of current and write down the equations of voltage and current.

3.

Find the impedance of a series RLC circuit if the inductive reactance, capacitive reactance and resistance are 184 Ω, 144 Ω and 30 Ω respectively. Also calculate the phase angle between voltage and current.

Answer 1

1) The voltage can be found by Ohm's law:

$$V=IX_L=I\omega L=I\cdot2\pi fL=15\text{ V}.$$

2) The capacitive reactance is

$$X_C=\frac{1}{2\pi fC}=98\space\Omega.$$

RMS value of current:

$$I=\frac{V}{X_C}=2.2\text{ A}.$$

3) The impedance of a series RLC circuit is

$$Z=\sqrt{(X_L-X_C)^2+R^2}=50\space\Omega.$$

The phase angle between voltage and current equals

$$\phi=\text{atan}\frac{X_L-X_C}{R}=53^\circ.$$