Question

Write about L-C-R Series (In 300 words).

Answer 1

The LCR circuit analysis can be understood better in terms of phasors. A phasor is a rotating quantity.
For an inductor (L), if we consider I to be our reference axis, then voltage leads by 90° and for the capacitor the voltage lags by 90°. But the resistance, current and voltage phasors are always in phase.
Analysis of an LCR circuit – series circuit

Let’s consider the following lcr circuit using the current across the circuit to be our reference phasor because it remains the same for all the components in a series lcr circuit.

From the above phasor diagram we know that,
V2 = (VR)2 + (VL – Vc)2          -------1
Now Current will be equal in all the three as it is a series LCR circuit. Therefore,
VR = IR       —– (2)
VL = IXL    —– (3)
Vc = IXc     —– (4)

Using (1), (2), (3) and (4)
I = V√R2 + (XL − XC)2
Also the angle between V and I is known phase constant,

tan ∅ = VL − VCVR

It can also be represented in terms of impedance,

tan ∅ = XL − XCR

Depending upon the values of XL and XCwe have three possible conditions,
i) If XL>Xc , then tan∅>0 and the voltage leads the current and the circuit is said to be inductive
ii) XL<Xc , then tan∅<0 and the voltage lags the current and the circuit is said to be capacitiveIf
iii) XL = Xc , then tan ∅ = 0 and the voltage is in phase with the current and is known as resonant circuit.

Answer 2

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