A) 2 : 1
B) 1 : 2
C) 2 : 9
D) 9 : 2
Correct Answer: C
Solution :
In series combination, the net resistance \[{{R}_{s}}=R+2R=3R\] Heat produced in \[{{R}_{s}}\], \[{{H}_{s}}=\frac{{{V}^{2}}}{{{R}_{s}}}=\frac{{{V}^{2}}}{3R}\] ? (i) In parallel combination, the net resistance \[{{R}_{p}}=\frac{R\times 2R}{R+2R}=\frac{2{{R}^{2}}}{3R}=\frac{2}{3}R\] Heat produced in \[{{R}_{p}}\], \[{{H}_{p}}=\frac{{{V}^{2}}}{{{R}_{p}}}=\frac{{{V}^{2}}}{2R/3}=\frac{3{{V}^{2}}}{2R}\] ? (ii) Dividing Eq. (i) by Eq. (ii), we obtain \[\frac{{{H}_{s}}}{{{H}_{p}}}=\frac{{{V}^{2}}/3R}{3{{V}^{2}}/2R}=\frac{2}{9}\]
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