Name: Purely Inductive Circuit
Uploaded: 2019-07-19
Duration: 5 min 40 s
Description: How does an inductor behave in a circuit? This video will explain every parameter involved in the derivation of a pure inductor working with AC supply.

Question

With the help of a phasor diagram, find an expression for impedance

(Z)

in a series

L - C - R

circuit.

Accepted Answer

Suppose the voltage across resistance $R$ is $V_{R}$ , the voltage across inductance $L$ is $V_{L}$ and the voltage across capacitance $C$ is $V_{c}$ . The voltage $V_{R}$ and current $I$ are in the same phase, the voltage $V_{L}$ will leads the current by angle $90^{°}$ while the voltage $V_{C}$ will lag behind the current by angle $90^{°}$ . Clearly $V_{C} and V_{L}$ are in opposite directions, therefore their resultant potential difference $= V_{L} - V_{C}$ here, $(V_{L} > V_{C})$ .

Thus $V_{R}$ and $(V_{L} - V_{C})$ are mutually perpendicular and the phase difference between them is $90^{°}$ . As the applied voltage across the circuit is $V$ , the resultant of $V_{R}$ and $(V_{L} - V_{C})$ will also be $V$ .

Its magnitude of $V$ is the phasor sum of $V_{R,} V_{L}$ and $V_{C}$ .

The phasor diagram for the circuit is as shown below

$\vec{\bar{V}} = {\vec{V}}_{R} + \vec{V_{C}} + {\vec{V}}_{L}$

From diagram,
$V^{2} = I^{2} [R^{2} + {(X_{L} - X_{C})}^{2}]$

As $I = \frac{V}{Z} = \frac{V}{\sqrt{R^{2} + (X_{L} - X_{C})^{2}}}$

By Comparing these equations

The impedance of an L-C-R circuit

$Z = \sqrt{R^{2} + (X_{L} - X_{C})^{2}}$

With the help of a phasor diagram, find an expression for impedance $(Z)$ in a series $L - C - R$ circuit.

Important Questions on Alternating Current

Learn and Prepare for any exam you want !

With the help of a phasor diagram, find an expression for impedance Z in a series L-C-R circuit.

Important Questions on Alternating Current

Learn and Prepare for any exam you want !

With the help of a phasor diagram, find an expression for impedance $(Z)$ in a series $L - C - R$ circuit.