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As shown in the figure an inductor of inductance $\mathrm{200 \: \mathrm{mH}}$ is connected to an AC source of emf $\mathrm{220 \mathrm{~V}}$ and frequency $\mathrm{50 \mathrm{~Hz}.}$ The instantaneous voltage of the source is $\mathrm{\mathrm{0} \mathrm{V}}$ when the peak value of current is $\mathrm{\frac{\sqrt{a}}{\pi}A.}$ The value of a is _________.

Option: 1
242

Option: 2
-

Option: 3
-

Option: 4
-

Answers (1)

best_answer

$\mathrm{L= 200\, mH}$
$\mathrm{V_{rms}= 220\, V}$
$\mathrm{f= 50\, Hz}$

For pure inductive ckt ,
Instantaneous current & voltage has phase difference of $\mathrm{\frac{\pi}{2}\, rad}$
(Current lags voltage by $\mathrm{\frac{\pi}{2}\, rad}$ )

$\mathrm{I_{0}=\text{ Peak value of current}= \frac{\sqrt{a}}{\pi}= \frac{V_{0}}{X_{L}}}$
              $\mathrm{\frac{\sqrt{a}}{\pi}= \frac{\sqrt{2}\times 220}{2 \pi\times 50\times 200\times 10^{-3}}}$
               $\mathrm{\sqrt{a}= 11\sqrt{2}}$
                $\mathrm{\sqrt{a}= \sqrt{242}}$

                  $\mathrm{a= 242}$

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manish painkra

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