In a coil of resistance $8 \,\Omega$, the magnetic flux due to an external magnetic field varies with time as $\phi=\frac{2}{3}\left(9-t^{2}\right)$. The value of total heat produced in the coil, till the flux becomes zero, will be _____________ $J$.
Answer (integer)
2
Solution
<p>$R = 8\,\Omega$</p>
<p>$\phi = {2 \over 3}(9 - {t^2})$</p>
<p>At $t = 3$, $\phi = 0$</p>
<p>$\varepsilon = \left| { - {{d\phi } \over {dt}}} \right| = {4 \over 3}t$</p>
<p>$$H = \int_0^3 {{{{V^2}} \over R}dt = \int_0^3 {{1 \over 8} \times {{16} \over 9}{t^2}dt} } $$</p>
<p>$$ = {2 \over 9} \times \left( {{{{t^3}} \over 3}} \right)_0^3 = {2 \over {9 \times 3}} \times 27 = 2\,J$$</p>
About this question
Subject: Physics · Chapter: Electromagnetic Induction · Topic: Faraday's Laws
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