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(B) The heat flow is given by $\Delta Q = \frac{\Delta T}{R_{eq}} t$,where $\Delta T$ is the temperature difference and $R_{eq}$ is the equivalent the

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$3$

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(B) The heat flow is given by $\Delta Q = \frac{\Delta T}{R_{eq}} t$,where $\Delta T$ is the temperature difference and $R_{eq}$ is the equivalent thermal resistance.For two identical rods of resistance $R$,the series resistance is $R_{series} = R + R = 2R$.For the series case,$\Delta Q = \frac{\Delta T}{2R} 	imes 12$.When joined in parallel,the equivalent resistance is $R_{parallel} = \frac{R 	imes R}{R + R} = \frac{R}{2}$.For the parallel case,$\Delta Q = \frac{\Delta T}{R/2} 	imes t$.Equating the two expressions for $\Delta Q$: $\frac{\Delta T}{2R} 	imes 12 = \frac{\Delta T}{R/2} 	imes t$.$\frac{12}{2R} = \frac{2t}{R} \Rightarrow 6 = 2t \Rightarrow t = 3 \, 	ext{minutes}$.

Two rods of same material have same length and area. The heat $\Delta Q$ flows through them for $12 \, \text{minutes}$ when they are joined in series. If now both the rods are joined in parallel,then the same amount of heat $\Delta Q$ will flow in ........ $\text{minutes}$.

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