Question

If the given circuit, power dissipation is 150w then R in ohms is​

Answer 1

We have been given a circuit having resistors of resistances R , 2 Ω's and having battery of 15 V

R Ω , 2 Ω are connected in parallel .

Power dissipation in the circuit (P) = 150 W

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If resistors are connected in parallel ,

$\sf \bigstar\ \; \dfrac{1}{R_{eq}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3}+...$

Power dissipation in the circuit is given by ,

$\sf \bigstar\ \; P=\dfrac{V^2}{R_{eq}}$

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Let ,

R₁ = R Ω  , R₂ = 2 Ω

$\to \sf \dfrac{1}{R_{eq}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}\\\\\to \sf \dfrac{1}{R_{eq}}=\dfrac{1}{R}+\dfrac{1}{2}\\\\\to \sf \dfrac{1}{R_{eq}}=\dfrac{2+R}{2R}\\\\\leadsto \sf R_{eq}=\dfrac{2R}{2+R}\ \; \pink{\bigstar}$

Power dissipation in the circuit (P) = 150 W

$\to \sf P=\dfrac{V^2}{R_{eq}}\\\\\to \sf 150=\dfrac{(15)^2}{\frac{2R}{2+R}}\\\\\to \sf 10=\dfrac{15(2+R)}{2R}\\\\\to \sf 10(2R)=30+15R\\\\\to \sf 20R=30+15R\\\\\to \sf 20R-15R=30\\\\\to \sf 5R=30\\\\\to \sf R=6\ \Omega\ \; \orange{\bigstar}$

Answer 2

We have been given a circuit having resistors of resistances R , 2 Ω's and having battery of 15 V

R Ω , 2 Ω are connected in parallel .

Power dissipation in the circuit (P) = 150 W

______________________________

If resistors are connected in parallel ,

Power dissipation in the circuit is given by ,

______________________________

Let ,

R₁ = R Ω  , R₂ = 2 Ω

Power dissipation in the circuit (P) = 150 W