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Heat produced in resistor due to inductor

1 vote

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 $LE^2 /2R_1 ^2$

asked Feb 9, 2017 in Physics Problems by koolman (4,286 points)
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

1 Answer

2 votes
Best answer

The energy stored by inductor would be released all in the resistance as heat
(as you may be doing in capacitors)

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$

answered Feb 9, 2017 by physicsapproval (2,320 points)
selected Feb 9, 2017 by koolman
But we have to find heat produced in resistance
you may read first line of answer :)
Is the answer given by me is also correct