What is the resistance to be connected in series with a condenser of a capacity 5 $μ F$ so that the phase diffe-rence between the current and the applied voltage is $45^{0}$ when the angular frequency of the applied voltage is 400 rad $s^{- 1}$

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$250 Ω$

$600 Ω$

$400 Ω$

$500 Ω$

answer is C.

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Detailed Solution

if the phase difference is 45⁰,

then the power factor of RC circuit is $C o s ϕ = \frac{R}{Z} = \frac{R}{\sqrt{R^{2} + {X_{C}}^{2}}} = 1 / \sqrt{2}$

$R = X_{C} = \frac{1}{ω C} = \frac{1}{400 \times 5 \times 10^{- 6}} = 500 Ω$

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