An arc lamp requires a direct current of 10 A at 80 V to function. If it is connected to a 220 V (rms), 50 Hz AC supply, the series inductor needed for it to work is close to :

Question

An arc lamp requires a direct current of 10 A at 80 V to function. If it is connected to a 220 V (rms), 50 Hz AC supply, the series inductor needed for it to work is close to : (A) 80 H (B) 0.08 H (C) 0.044 H (D) 0.065 H

Tardigrade Admin · Accepted Answer

For dc

R = (80/10) = 8 ω For ac

10 = (220/√R2 + ω2L2) R2 + ω2L2 = ((220/10))2 L2 = (222 - 82/ω2) ∴ L = (√30 ×14/2 π×50) = (√420/100 π) = 0.065 H

Q. An arc lamp requires a direct current of $10 A$ at $80 V$ to function. If it is connected to a $220 V (r m s)$ , $50 Hz A C$ supply, the series inductor needed for it to work is close to :

80 H

0.08 H

0.044 H

0.065 H

For $d c$

$R = \frac{80}{10} = 8 ω$
For $a c$

$10 = \frac{220}{R ^{2} + ω ^{2} L ^{2}}$
$R^{2} + ω^{2} L^{2} = (\frac{220}{10})^{2}$
$L^{2} = \frac{2 2 ^{2} - 8 ^{2}}{ω ^{2}}$
$∴ L = \frac{30 \times 14}{2 π \times 50} = \frac{420}{100 π} = 0.065 H$

Q. An arc lamp requires a direct current of 10A at 80V to function. If it is connected to a 220V(rms), 50HzAC supply, the series inductor needed for it to work is close to :