The frequency at which the inductive reactance of 2H inductance will be equal to the capacitive reactance of 2 μ F capacitance (nearly)

Question

The frequency at which the inductive reactance of 2H inductance will be equal to the capacitive reactance of 2 μ F capacitance (nearly) (A) 80Hz (B) 40 Hz (C) 60Hz (D) 20Hz

Tardigrade Admin · Accepted Answer

X L = X C W L =(1/ WC ) W 2=(1/ LC ) W =√(1/ LC ) f =(1/2 π) √(1/ LC ) =(1/2 π) √(1/2 × 2 × 10-6) =(1/2 π) × (1/2 × 10-3) =(103/4 π) =80 Hz

Q. The frequency at which the inductive reactance of 2H inductance will be equal to the capacitive reactance of $2 μ F$ capacitance (nearly)

80Hz

40 Hz

60Hz

20Hz

$X_{L} = X_{C}$
$W L = \frac{1}{W C}$
$W^{2} = \frac{1}{L C}$
$W = \frac{1}{L C}$
$f = \frac{1}{2 π} \frac{1}{L C}$
$= \frac{1}{2 π} \frac{1}{2 \times 2 \times 1 0 ^{- 6}}$
$= \frac{1}{2 π} \times \frac{1}{2 \times 1 0 ^{- 3}}$
$= \frac{1 0 ^{3}}{4 π}$
$= 80 Hz$

Q. The frequency at which the inductive reactance of 2H inductance will be equal to the capacitive reactance of 2μF capacitance (nearly)