1.

Three resistors R_1, R_2 and R_3 are to be combined to form an electrical circuit as shown in the figure. It is found that when R_1 R_2 and R_3 are put respectively in positions A, B and C, the effective resistance of the circuit is 70 OmegaWhen R_2, R_3 and R_1 are put respectively in position A, B and C the effective resistance is 35Omega and when R_3, R_1 and R_2 are respectively put in the position A, B and C, the effective resistance is 42 Omega The resistance R_(1): R_(2): R_(3 )are in the ratio

Answer»

0.04380787037037
0.043101851851852
0.043854166666667
0.043819444444444

Solution :According to the condition of the PROBLEM`(R_(1)R_(2)+R_(2)R_(3)+R_(3)R_(1))/(R_(1)+R_(2))=70ldots(1)`
`(R_(2)R_(3)+R_(3)R_(1)+R_(1)R_(2))/(R_(2)+R_(3))35ldots(2)`
`(R_(3)R_(1)+R_(1)R_(2)+R_(2)R_(3))/(R_(3)+R_(1))=42ldots(3)`
`(R_(1)R_(2)+R_(2)R_(3)+R_(3)R_(1))=k`
Then the SYSTEM of three equation transforms to`R_(1)+R_(2)=(k)/(70)`
`R_(2)+R_(3)=(k)/(35)R_(3)+R_(1)=(k)/(42)`
Solving, this we get`R = k//210, R = k//105, R = 2k//105`
`impliesR_(1): R_(2): R_(3) = 1:2:4`
So, let `R_(1) = x, R_(2) = 2x` and `R_(3) = 4x`
Putting these valued in equation 1, we get`X = 15`
`R_(1) = 15, R_(2) = 30, R_(3) = 60`


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