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Standard X

Physics

Domestic Electric Circuits

An arc lamp r...

Question

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

0.08 H

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0.044 H

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0.065 H

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80 H

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Solution

The correct option is C $0.065 H$
For DC

$R = \frac{V}{I} = \frac{80}{10} = 8 Ω$

For AC
$I = 10 A$

$I = \frac{V}{R}$

$10 = \frac{220}{\sqrt{R^{2} + ω^{2} L^{2}}}$

$R^{2} + ω^{2} L^{2} = 484$

$L^{2} = \frac{484 - 64}{2 π ν}$

$L^{2} = \frac{420}{2 \times 3.14 \times 50}$

$L = 0.065 H$

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An arc lamp requires a direct current of 10 A and 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 :

The correct option is C 0.065 HFor DC R=VI=8010=8Ω For ACI=10A I=VR 10=220√R2+ω2L2 R2+ω2L2=484 L2=484−642πν L2=4202×3.14×50 L=0.065H

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

The correct option is C $0.065 H$
For DC

$R = \frac{V}{I} = \frac{80}{10} = 8 Ω$

For AC
$I = 10 A$

$I = \frac{V}{R}$

$10 = \frac{220}{\sqrt{R^{2} + ω^{2} L^{2}}}$

$R^{2} + ω^{2} L^{2} = 484$

$L^{2} = \frac{484 - 64}{2 π ν}$

$L^{2} = \frac{420}{2 \times 3.14 \times 50}$

$L = 0.065 H$