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In a Whatstone's bridge all the four arm...

In a Whatstone's bridge all the four arms have equal resistance `R_(0)`. If the resistance of the galvanometer arm is `2R_(0)`, the equivalent resistance of the combination as seen by the battery is

A

`R_(0)`

B

`2R_(0)`

C

`(R_(0))/(4)`

D

`(R_(0))/(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
As bridge is in balanced condition, no current will flow through BD.
`R_(1)=R_(AB)+R_(BC)=R_(0)+R_(0)=2R_(0)`
`R_(2)=R_(AD)+R_(CD)=R_(0)+R_(0)=2R_(0)`
Also, `R_(1) and R_(2)` are in paralel combination.
Hence, equivalent resistance between A and C will be

`R_(eq)=(R_(1)R_(2))/(R_(1)+R_(2))=(4R_(0)^(2))/(4R_(0))=R_(0)`
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