(a) Write the mathematical expression for Joule's law of heating.(b) Compute the heat generated while transferring 96000 coulomb of charge in two hours through a potential difference of 40 V.

(a) Mathematical expression for Joule's law of heating is:

$H=I^2Rt$

Where,

$H$ = Heating effect.

$I$ =  Current flowing through the conductor.

$R$ = Amount of electric resistance in the conductor.

$t$ = Time taken.

(b) Given:

Volatge, $V$ = 40 V

Charge, $Q$ = 96000 C

Time, $t$ = 2 hour

To find: Heat generated, $H$.

Solution:

We know that formula for heat generated is:

$H=I^2Rt$

This formula can be deduced for Q as-

$H=I^{2}\frac {V}{I}t$      $(\because R=\frac {V}{I})$

$H=IVt$

Now,

$H=\frac {Q}{t}Vt$          $(\because I=\frac {Q}{t})$

$H=QV$

Substituting the given values in the above formula, we get-

$H=QV$

$H=96000\ C\times {40\ V}$

$H=3,840,000\ J $

$H=3.84\times {10^6}\ J $

Thus, the heat generated while transferring 96000 coulombs of charge in two hours through a potential difference of 40 is $3.84\times {10^6}\ J$.

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Updated on: 10-Oct-2022

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