A) 10/3
B) 10
C) 30
D) 90
Correct Answer: D
Solution :
Key Idea: Power is the rate at which energy is transferred. Power \[=\frac{\Delta U}{\Delta t}=V\frac{\Delta q}{\Delta t}=Vi\] or \[P=Vi=\frac{{{V}^{2}}}{R}\] \[(\because \,V=i\,R)\] When resistors are in parallel, then \[{{R}_{1}}=R+R+R=3R\] \[\therefore \] Power dissipated \[{{P}_{1}}=\frac{{{V}^{2}}}{{{R}_{1}}}=\frac{{{V}^{2}}}{3R}\] When resistors are in parallel, then \[\frac{1}{{{R}_{2}}}=\frac{1}{R}+\frac{1}{R}+\frac{1}{R}=\frac{3}{R}\] \[\Rightarrow {{R}_{2}}=\frac{R}{3}\] \[\therefore {{P}_{2}}=\frac{{{V}^{2}}}{{{R}_{2}}}=\frac{{{V}^{2}}}{R/3}=\frac{3{{V}^{2}}}{R}\] Therefore, \[{\frac{{{P}_{2}}}{{{P}_{1}}}=\frac{3{{V}^{2}}}{R}}/{\frac{{{V}^{2}}}{3R}}\;=9\] \[{{P}_{2}}=9{{P}_{1}}=9\times 10\] = 90 watt
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