Question

Question 2
In the following circuits (figure), heat produced in the resistor or combination of resistors connected to a 12V battery will be


(a) same in all the cases
(b) minimum in case (i)
(c) maximum in case (ii)
(d) maximum in case (iii)

Answer 1

(d) maximum in case (iii)

Heat produced $=\left(\frac{V^2}{R}\right)t$

Case (i) R = 2$\Omega$, V=12V
$Heat=\left(\frac{{12}^2}{2}\right)t=72t$

Case (ii) R =2+2 = 4$\Omega$, V = 12V
$Heat=\left(\frac{{12}^2}{4}\right)t=36t$

Case (iii) $R=\frac{2\times 2}{2+2}$=1$\Omega$, V = 12V
$Heat=\left(\frac{{12}^2}{1}\right)t=144t$

Therefore the maximum heat produced is in (iii) and the minimum heat produced is in (ii).