Two-30-ohms-resistor-are-connected-in-parallel-what-should-be-the-resistance-to-be-connected-in-series-with-this-parallel-combination-such-that-the-power-in-each-30-ohms-is-1-4-th-of-total-power-

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Question Number 14962 by tawa tawa last updated on 06/Jun/17

$$\mathrm{Two}30\mathrm{ohms}\mathrm{resistor}\mathrm{are}\mathrm{connected}\mathrm{in}\mathrm{parallel},\mathrm{what}\mathrm{should}\mathrm{be}\mathrm{the}\mathrm{resistance}$$$$\mathrm{to}\mathrm{be}\mathrm{connected}\mathrm{in}\mathrm{series}\mathrm{with}\mathrm{this}\mathrm{parallel}\mathrm{combination}\mathrm{such}\mathrm{that}\mathrm{the}\mathrm{power}$$$$\mathrm{in}\mathrm{each}30\mathrm{ohms}\mathrm{is}\frac{1}{4}\mathrm{th}\mathrm{of}\mathrm{total}\mathrm{power}.$$

Answered by ajfour last updated on 06/Jun/17

$$\frac{P}{4}=I^{2}R,P=2I^{2}R+{\left(2I\right)}^{2}x$$$$\Rightarrow 4I^{2}R=2I^{2}R+4I^{2}x$$$$x=\frac{2I^{2}R}{4I^2}=\frac{R}{2}=\frac{30\mathrm{\Omega }}{2}=15\mathrm{\Omega }.$$

Commented by tawa tawa last updated on 06/Jun/17

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$

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