# Heat produced in resistor due to inductor

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In the circuit shown, initially the switch is in position 1 for a long time. Then the switch is shifted to position 2 for a long time. Find the total heat produced in R$_2$.

After long time in positin1 the current inthe circuit is E/R$_1$
So in position 2 alsote current frm inductor would be E / R$_1$
Hence the heat produced in R$_2$ would be $ER_2 ^2/R_1$

But the answer given as $LE^2 /2R_1 ^2$

In position 2 the current is initially $I_0=E/R_1$ but it does not remain at this value, it decays exponentially. How long it takes to decay depends on the energy stored in the inductor.

The initial *power* generated in $R_2$ is $I_0^2 R_2$ Watts - *not* $I_0 R_2^2$. But you are asked for the total *heat energy* dissipated in $R_2$ in Joules.
Thanks a lot

The energy stored by an inductor is$1/2LI^2$
your $I$ is correct
hence putting that in above equation you would get the answer hence this heat would be same for resistance. And hence answer would be$LE^2/2(R_1)^2$