Question

$100\;J$ of heat is produced each second in a $4\Omega$ resistance. Find the potential difference across the resistor.

Answer 1

Hint : To find the potential difference, we can use the equation of heat containing the potential difference and resistance as the components. By substituting the values and simplifying, we can easily find the value of potential difference.

Complete Step By Step Answer:
Let us note down the given data as follows:
$Q = 100J$ , $R = 4\Omega$ , $t = 1s$ , $V = ?$
Now, we know that the general power equation is $P = VI$
Where, $P$ = Power consumption in the resistor = Heat generated per unit time
$\therefore \dfrac{Q}{t} = VI$
$\therefore Q = VIt$
From Ohm’s Law, $V = IR$
$\therefore I = \dfrac{V}{R}$
Substituting this value in the heat equation,
$\therefore Q = \dfrac{{{V^2}}}{R}t$
Now, substitute the values given in the data,
$\therefore 100J = \dfrac{{{V^2}}}{{4\Omega }}(1\sec )$
Shifting the equation to make potential difference the subject of the equation,
${V^2} = 100J \times 4\Omega$
$\therefore {V^2} = 400$
Applying square root on both sides,
$\therefore V = 20V$
Thus, the potential difference across the resistor is $20\;V$ .

Additional Information:
The heat produced by the resistor is known as Joule Heating. Joule Heating is the phenomenon or a process by which heat is generated by the passing of electric current through the resistor. The Joule heating is proportional to the product of the resistance and the square of the current passing through the resistance. Joule heating is helpful in some cases like Electric Iron, Electric Heater, etc. whereas it is wanted in the transfer of electric current through wires.

Note :
In the above question, the electric current passed required to produce the given heat can also be found by changing the heat equation as follows.
We know, power consumption is $P = VI$ . From Ohm’s Law, $V = IR$
Thus, for removing the potential difference from the equation,
$\therefore P = (IR)I$
$\therefore P = {I^2}R$
Hence, by this formula, the current required for the given heat generation can also be found.