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  • For ensuring dissipation of same energy in all three resistors <img alt="\left(\mathrm{R}_1, \mathrm{R}_2, \mathrm{R}_3\right)" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cleft%28%

For ensuring dissipation of same energy in all three resistors \left(\mathrm{R}_1, \mathrm{R}_2, \mathrm{R}_3\right) connected as shown in figure, their values must be related as:

Option: 1

\mathrm{R_1=R_2=R_3}


Option: 2

\mathrm{\mathrm{R}_2=\mathrm{R}_3 \text{ and } \mathrm{R}_1=4 \mathrm{R}_2}


Option: 3

\mathrm{\mathrm{R}_2=\mathrm{R}_3 \text{ and }\mathrm{R}_1=\frac{\mathrm{R}_2}{4}}


Option: 4

\mathrm{\mathrm{R}_1=\mathrm{R}_2+\mathrm{R}_3}


Answers (1)

best_answer

As voltage across the resistors \mathrm{\mathrm{R}_2 \text { and } \mathrm{R}_3} is same and they show same dissipation of energy, so using the relation for energy \mathrm{H=\frac{V^2}{R} t}, we get \mathrm{\mathrm{R}_2=\mathrm{R}_3}

Thus, the current in each resistor \mathrm{\mathrm{R}_2 \text{ and }\mathrm{R}_3} will be \mathrm{\frac{I}{2}}.

\mathrm{\text { i.e., } I_1=\frac{I}{2} \text { and } I_2=\frac{I}{2}}

Since the energy dissipation is same in all the three resistors, so

 \mathrm{I}^2 \mathrm{R}_1 \mathrm{t}=\mathrm{I}_{1}^2 \mathrm{R}_2 \mathrm{t}

Or     \mathrm{I}^2 \mathrm{R}_1 \mathrm{t}=\left(\frac{\mathrm{I}}{2}\right)^2 \mathrm{R}_2 \mathrm{t}

Or     \mathrm{R}_1=\frac{\mathrm{R}_2}{4}

Posted by

Rishi

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