Question

An alternating voltage E E sin wt = o is applied to a circuit comprising of an inductor (L),
a capacitor (C) and a resistor (R) in series. Obtain an expression for (i) impedence of the
circuit and (ii) phase angle between voltage and current

Answer 1

Z = R + j (ωL + 1/ωC); Phase angle = tan-1 ((1+ωLC)/ (ωCR))

Explanation:  

The circuit which has R, L, and C in series is a series resonant circuit. It has many applications but its best application is in high voltage. It is used to create high voltage at resonance frequency for the testing of equipment. Now, we will calculate its impedance and phase angle.

As the circuit is in series so all reactive components and resistance will add.

Z = R + j (ωL + 1/ωC)

And,  

Phase angle = tan-1 ((1+ωLC)/ (ωCR))

Answer 2

Explanation:

An alternating voltage is given by :

$E=E_o\sin\omega t$

If L is the inductor, C is a capacitor and R is a resistor, then the impedance of the circuit is given by the formula as follows :

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

Here,

$X_L=\omega L\\\\X_C=\dfrac{1}{\omega C}$

The phase angle between voltage and the current is given by :

$\phi=\tan^{-1}(\dfrac{X_L-X_C}{R})$

Hence, this is the required solution.