A parallel plate capacitor in series with a resistance of 100 W, an inductor of 20 mH and an AC voltage source of variable frequency shows resonance at a frequency of (1250/π)HZ. If this capacitor is charged by a DC voltage source to a voltage 25 V, what amount of charge will be stored in each plate of the capacitor?

Question

A parallel plate capacitor in series with a resistance of 100 W, an inductor of 20 mH and an AC voltage source of variable frequency shows resonance at a frequency of (1250/π)HZ. If this capacitor is charged by a DC voltage source to a voltage 25 V, what amount of charge will be stored in each plate of the capacitor? (A) 0.22 mC (B) 2 mC (C) 0.2 mC (D) 0.2 C

Tardigrade Admin · Accepted Answer

ω0 =2π f0 =(1/√LC) ⇒ 4π2×(1250×1250/π2) =(1/20×10-3× c) ∴ C=(1000/20×4×1250×1250) =8×10-6F | Qss =CV =8×10-6 ×25 =0.2mc

0.22 mC

2 mC

0.2 mC

0.2 C

ω0​=2πf0​=LC​1​⇒4π2×π21250×1250​=20×10−3×c1​ ∴C=20×4×1250×12501000​=8×10−6F ∣Qss​=CV=8×10−6×25=0.2mc

$ω_{0} = 2 π f_{0} = \frac{1}{L C} \Rightarrow 4 π^{2} \times \frac{1250 \times 1250}{π ^{2}} = \frac{1}{20 \times 1 0 ^{- 3} \times c}$
$∴ C = \frac{1000}{20 \times 4 \times 1250 \times 1250} = 8 \times 1 0^{- 6} F$
$∣ Q_{ss} = C V = 8 \times 1 0^{- 6} \times 25 = 0.2 m c$