A) 10/3
B) 10
C) 30
D) 90
Correct Answer: A
Solution :
| [a] 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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