An amount of charge Q passes through a coil of resistance R.... | Physics | SolveeIt

Question

An amount of charge Q passes through a coil of resistance R.If the current in the coil decreases to zero at a uniform rate during time T, then the amount of heat generated in the coil will be,

$\frac{4Q^2R}{3T}$

$\frac{2QR}{3T}$

$\frac{Q^2T}{4R}$

$Q^2RT$

Answer

$\frac{4Q^2R}{3T}$

Explanation

Solution

The correct answer is option (A): $\frac{4Q^2R}{3T}$
The corresponding
i−t graph will be a straight line with
i decreasing from a peak value
(say i)to zero in time t.
∴ $i=i-(\frac{i}{t})t$
(y=−mx+c)……(i)
$i=\frac{2q}{t}$
Now, at time t, heat produced in a short interval dt is,
dH=i2Rdt
$\Rightarrow dH=(\frac{2q}{t}-\frac{2qt^2}{t^2})Rdt$
∴ Total heat produced,
$\int_{0}^{H}dH=\int_{0}^{t}(\frac{2q}{t}-\frac{2qt^2}{t^2})Rdt$
$\Rightarrow H=\frac{4q^2R}{3t}$

Physics Question on Electromagnetic induction

Solution