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A balanced Wheatstone bridge has resista...

A balanced Wheatstone bridge has resistances `100Omega , 10Omega, 500Omega and 50 Omega` repectively in its four arms. Determine the ratio of powers consumed in its different arms.

Text Solution

Verified by Experts

In Fig . 3.7 , Wheatstone bridge has been shown .

Let `I_(1)=(V)/(P+Q)andI_(1)=(V)/(R+S)`
`therefore(I_(1))/(I_(2))=(R+S)/(P+Q)=(500+50)/(100+10)=5" or , " I_(1)=5I_(2)`
`therefore` The required ratio
`=I_(1)^(2)P:I_(1)^(2)Q:I_(2)^(2)R:I_(2)^(2)S:`
`=(5I_(2))^(2)xx100:(5I_(2))^(2)xx10:I_(2)^(2)xx500:I_(2)^(2)xx50`
= `2500:250:500:50=50:5:10:1`
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