Question

(a) Write down the formula for the heat produced when a current I si passed through a resistor R for time t.
(b) An electric iron of resistance 20 ohms draws a current of 5 amperes. Calculate the heat produced in 30 seconds.

Answer 1

a) Consider a resistor of Resistance R. Let the current flowing through the resistor be I and the potential difference across its ends be V.
In time t, let Q amount of charge flows through the resistor.

Work done on Moving charge will be,
$W=V\times Q$ ---------(1).

According to the definition of electric current,
$Q=I\times t$ -----------(2).

Putting equation (2) in (1),
$W=V\times I\times t$
And the work done is dissipated as heat.
Therefore,
Heat produced, $H=W=V\times I\times t=VIt$
$H=VIt$
According to Ohm's law $V=I\times R$
Putting this in equation (2), we get,
$H=IR\times It$
Therefore, $Heat=I^{2}Rt$


b) (R) = 20 Ω
(I)= 5 A
(t)= 30 s

Now we know that $H=I^{2}Rt$

use it here $H=5\times 5\times 20\times 30$

= 15000J

$H=1.5\times {10}^{4}J$

The heat developed in 30 s is $H=1.5\times {10}^{4}J$