Question

A solenoid with inductance L=7mH and active resistance R=44_∩_ is first connected to a source of direct voltage V° and then source of sinusoidal voltage with effective value V=V°. At what frequency of the oscillator will the power consumed by the solenoid be n=5.0 times less than in the former case?

Answer 1

Answer:

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Answer 2

$\bold {\huge {Answer :-}}$

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Given →

⇨ Inductor (L) = 7 mH

⇨ Resistance (R)= 44 ohm

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Power is given by

✭In DC Source✭

$\large{\boxed{\sf\:{P_{DC}=\frac{V_\circ^2}{R}}}}$

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✭In AC source✭

$\large{\boxed{\sf\:{P_{AC}=\frac{V_\circ^2. R}{R^2+\omega^2.L^2}}}}$

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$\large{\boxed{\sf\:{P_{AC}= \frac{1}{5}P_{DC}}}}\:\:\:\:\:\:\:\:\:[Given] \\\\\Rightarrow\large{\frac{V_\circ^2. R}{R^2+\omega^2.L^2}}=\frac{1}{5}{\frac{V_\circ^2}{R}}\\\\\Rightarrow\:5R^2= R^2+\omega^2.L^2\\\Rightarrow\:\omega=\frac{2R}{L}\\\Rightarrow2\pi\:f=\frac{2R}{L}\\\Rightarrow\:f = \frac{R}{\pi\:L}\\on\:putting\:the\:values \\\Rightarrow\:f= \frac{44}{(22/7) .7\times10^{-3}}\\\Rightarrow\:f = 2 \:\:KHz$

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Therefore, the frequency of the oscillator is 2 KHz