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

A series L-C-R circuit with

R = 60 Ω, L = 80 H and C = 5 μF

is connected to a variable frequency

240 V

supply. Calculate angular frequency, impedance and current at resonance condition.

Accepted Answer

Given The Inductance of the inductor, $L = 80.0 H$ .

The capacitance of the capacitor, $C = 5 μF = 5 \times 10^{- 6} F$ .

Resistance of the resistor, $R = 60 Ω$ .

Potential of the variable voltage source, $V = 240 V$ .

The resonance angular frequency is given as: $ω_{r} = \frac{1}{\sqrt{LC}} = \frac{1}{\sqrt{80 \times 5 \times 10^{- 6}}} = 50 rad / s$

Hence, the circuit will come in resonance for a source frequency of

$50 rad / s$ .

The impedance of the circuit is given by the relation:

$Z = \sqrt{R^{2} + {(X_{L} - X_{C})}^{2}}$ , where $X_{L,} X_{C}$ are the impedance of inductive resistance and capacitive resistance respectively.

At resonance $X_{L} = X_{C}$ , hence we get,

$Z = R = 60 Ω$ ...............................................(A)

At resonance, the peak voltage $V_{\max} = \sqrt{2} V = \sqrt{2} \times 240 V$ .

Therefore, the peak current,

$I_{\max} = \frac{V_{\max}}{Z} = \frac{\sqrt{2} \times 240}{60} = 5.64 A$ ........................(B)

Hence, at the resonance, the impedance= $60 Ω$ and current = $5.64 A$ and the angular velocity is $50 rad / \sec .$

A series L-C-R circuit with $R = 60 Ω, L = 80 H and C = 5 μF$ is connected to a variable frequency $240 V$ supply. Calculate angular frequency, impedance and current at resonance condition.

Important Questions on Alternating Current

Learn and Prepare for any exam you want !

A series L-C-R circuit with R=60Ω ,L=80 H and C=5μF is connected to a variable frequency240 V supply. Calculate angular frequency, impedance and current at resonance condition.

Important Questions on Alternating Current

Learn and Prepare for any exam you want !

A series L-C-R circuit with $R = 60 Ω, L = 80 H and C = 5 μF$ is connected to a variable frequency $240 V$ supply. Calculate angular frequency, impedance and current at resonance condition.