• question_answer
                    Three equal resistors connected in series across .a source of emf together dissipate 10 watt of power. What will be the power dissipated in watt if the same resistors are connected in parallel across the same source of emf?

    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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