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(D) The heat produced in a circuit is given by the formula $H = \frac{V^2}{R} 	imes t$,where $V$ is the potential difference,$R$ is the equivalent re

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maximum in case $(iii)$

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(D) The heat produced in a circuit is given by the formula $H = \frac{V^2}{R} 	imes t$,where $V$ is the potential difference,$R$ is the equivalent resistance,and $t$ is the time.Since $V = 12\, V$ is constant for all cases,the heat produced $H$ is inversely proportional to the equivalent resistance $R$ $(H \propto \frac{1}{R})$.Case $(i)$: $A$ single resistor of $2\, \Omega$. Equivalent resistance $R_1 = 2\, \Omega$.Case $(ii)$: Two resistors of $2\, \Omega$ each connected in series. Equivalent resistance $R_2 = 2\, \Omega + 2\, \Omega = 4\, \Omega$.Case $(iii)$: Two resistors of $2\, \Omega$ each connected in parallel. Equivalent resistance $R_3 = \frac{2 	imes 2}{2 + 2} = \frac{4}{4} = 1\, \Omega$.Comparing the resistances: $R_3 (1\, \Omega) Since $H \propto \frac{1}{R}$,the heat produced will be maximum where the resistance is minimum.Therefore,the heat produced is maximum in case $(iii)$ because it has the lowest equivalent resistance $(1\, \Omega)$.

In the following circuits (Figure),heat produced in the resistor or combination of resistors connected to a $12\, V$ battery will be

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