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In the given network, if an ideal batter...

In the given network, if an ideal battery is connected between points A and B, a current `i_1=5.6A` flows through the battery. If the same battery is connected between points B and C, a current `i_2=10.5A` flows through the battery. The value of `R_1/R_2=`

Text Solution

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Let EMF of battery =V
`i_1=V/((R_1(R_1+2R_2))/(2R_1+R_2))=5.6, i_2=V/((R_2(R_2+2R_1))/(2R_1+2R_2))=10.5`
Dividing the equations to eliminate V,
`(R_2(R_2+2R_1))/(R_1(R_1+2R_1))=8/15 implies (1+(2R_1)/R_2))/((R_1/R_2)(R_1+R_2+2))=8/5`
Let `R_1/R_2=x implies 15+30x=8x^2+16x, 8x^2-14x-15=0 implies x=5/2`
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