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 at 1000 Hz:

$$V=IZ,$$

where

$$Z=X_L=2\pi fL.$$

Therefore:

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

2. The capacitive reactance can be found as

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

The equations that ties voltage and current:

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

3. The impedance of the series RLC circuit:

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

The phase angle between the voltage and current vectors:

$$\theta=\text{tan}^{-1}\frac{X_L-X_C}{R}=53^\circ.$$