A) 4 :1
B) 1 : 3
C) 1 : 2
D) 2:1
Correct Answer: A
Solution :
If the wire are first connected in series the equivalent resistance is \[{{R}_{s}}=R+R=2R\] And if connected in parallel, the equivalent resistance is \[{{R}_{P}}=\frac{R\times R}{R+R}=\frac{R}{2}\] The heat produced by the current is \[H={{i}^{2}}Rt\propto R\] Hence, \[\frac{{{H}_{S}}}{{{H}_{P}}}=\frac{{{R}_{S}}}{{{R}_{P}}}=\frac{2R}{R/2}=\frac{4}{1}\] So, \[{{H}_{S}}:{{H}_{P}}=4:1\]
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