If power dissipated in the $9 \Omega$ resistor in the circuit shown is $36 \mathrm{~W}$, the potential…

If power dissipated in the $9 \Omega$ resistor in the circuit shown is $36 \mathrm{~W}$, the potential difference across the $2 \Omega$ resistor is
  1. $8 \mathrm{~V}$
  2. $10 \mathrm{~V}$
  3. $2 \mathrm{~V}$
  4. $4 \mathrm{~V}$

Solution

Electric power, $P=i^2 R$ $\therefore$ Current, $\quad i=\sqrt{\frac{P}{R}}$ For resistance of $9 \Omega$ $i_1=\sqrt{\frac{36}{9}}=\sqrt{4}=2 \mathrm{~A}$ $\begin{aligned} i_2 & =\frac{i_1 \times R}{6}=\frac{2 \times 9}{6}=3 \mathrm{~A} \\ i & =i_1+i_2=2+3=5 \mathrm{~A} \\ V_2 & =I R_2=5 \times 2=10 \mathrm{~V} \end{aligned}$

Asked in: NEET 2011 (Screening)

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