A 100 Ω resistance, a 0.1 μ F capacitor and an inductor are connected in series across a 250 V supply at variable frequency. Calculate the value of inductance of inductor at which resonance will occur. Given that the resonant frequency is 60 Hz.

Question

A 100 Ω resistance, a 0.1 μ F capacitor and an inductor are connected in series across a 250 V supply at variable frequency. Calculate the value of inductance of inductor at which resonance will occur. Given that the resonant frequency is 60 Hz. (A) 0.70 H (B) 70.3 mH (C) 7.03 × 10-5 H (D) 70.3 H

Tardigrade Admin · Accepted Answer

C=0.1 μ F=10-7 F Resonant frequency =60 Hz ωo=(1/√L C) 2 π f0=(1/√L C) ⇒ L=(1/4 π2 f02 C) by putting values L ≃ 70.3 Hz

Q. A $100 Ω$ resistance, a $0.1 μ F$ capacitor and an inductor are connected in series across a $250 V$ supply at variable frequency. Calculate the value of inductance of inductor at which resonance will occur. Given that the resonant frequency is $60 Hz$ .

$0.70 H$

$70.3 m H$

$7.03 \times 1 0^{- 5} H$

$70.3 H$

$C = 0.1 μ F = 1 0^{- 7} F$
Resonant frequency $= 60 Hz$
$ω_{o} = \frac{1}{L C}$
$2 π f_{0} = \frac{1}{L C}$
$\Rightarrow L = \frac{1}{4 π ^{2} f _{0}^{2} C}$
by putting values $L ≃ 70.3 Hz$

Q. A 100Ω resistance, a 0.1μF capacitor and an inductor are connected in series across a 250V supply at variable frequency. Calculate the value of inductance of inductor at which resonance will occur. Given that the resonant frequency is 60Hz.

0.70H

70.3mH

7.03×10−5H

70.3H