Question

Explain the series L-C-R circuit under the following heads.
(i) Resultant Voltage (ii) Impedance of circuit
(ii) Phase Difference between resultant voltage and current
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Answer 1

Answer:

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Answer 2

Explanation of LCR circuit:

From the given phasor diagram we know that,

V^2 =(VR)^2 + (VL – Vc)^2   —– (1)  (Resultant voltage)

Current will be equal in all the three as it is a series LCR circuit.

VR = IR—– (2)

VL = IXL —– (3)

Vc = IXc —– (4)

Using equations (1), (2), (3) and (4)

I = V√R2 + (XL − XC)2

The angle between V and I is known phase constant,

tan ∅ = VL − VCV

It can also be represented in terms of impedance,

tan ∅ = XL − XCR  (Impedance of circuit)

Depending upon the values of XL and XC we have three possible conditions for phase difference between resultant voltage and current,

If XL>Xc, then tan∅>0 and the voltage leads the current, the circuit is inductive.

If XL<Xc , then tan∅<0 and the voltage lags the current, circuit is capacitive

If XL =Xc , then tan ∅ = 0 and the voltage is in phase with the current, the circuit is resonant.