Consider the following circuit:For what value of, the circuit

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Consider the following circuit:

For what value of, the circuit shown above exhibits unity power factor?

1. 1
  LC
2. 1
  LC – R²C²
3. 1
  [LC + R²C²]
4. 1
  RC

Correct Option: B

For unity power factor: Circuit should have pure resistance. ...
∵ This condition will arise when, resonance takes place. When,
Y = G + JB and B = 0

Y =	1	+	1
	R – JX_C		JX_L

or Y =	R + JX_C	-	1
	R² + X_C²		X_L

or Y =	R	+ J		X_C	-	1
	R² + X_C²			R² + X_C²		X_L

For resonance

X_C	=	1
R² + X_C²	=	X_L

X_{C_{X_L = R² + X_C²
L = R² + 1
C ω²C²

L - R² = 1
C ω²C²

L – R²C = 1
C ω²C²

ω² = 1
ω²C²

ω² = 1
LC – R²C²

or ω = 1
√LC – R²C²}}