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Two resistances R1 and another R2 of the...

Two resistances `R_1` and another `R_2` of the same material but twice the length and half the thickness are connected in series with a standard battery E of internal resistance r. The balancing point is-

A

`1/(8l)`

B

`1/(4l)`

C

8l

D

16 l

Text Solution

Verified by Experts

The correct Answer is:
C
`R_(1)/R_(2) = (rho l)/r^(2) ((r/2)^(2))/(rho 2l) rArr R_(2) = 8R_(1)`
`phi = V_(0)/L_(0)` (Potential gradient)
`phi l = (ER_(1))/(r + R_(1) + R_(2)) = (ER_(1))/(r + 9R_(1))`
`phi l^(.) = (ER_(2))/(r + R_(1) + R_(2)) = (ER_(2))/(r + 9R_(1)) = (E8R_(1))/(R + 9R_(1))`
`l^(.)/l = 8 rArr l^(.) = 8l`
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