A) R
B) 2R
C) \[\frac{R}{4}\]
D) \[\frac{R}{2}\]
Correct Answer: A
Solution :
[a] Key Idea: The balanced condition of Wheat-stones bridge is, |
\[\frac{{{R}_{AB}}}{{{R}_{BC}}}=\frac{{{R}_{AD}}}{{{R}_{DC}}}\] |
As bridge is in balanced condition, no current will flow through BD. |
\[{{R}_{1}}={{R}_{AB}}+{{R}_{BC}}\] |
\[=R+R=2R\] |
\[{{R}_{2}}={{R}_{AD}}+{{R}_{CD}}=R+R=2R\] |
\[{{R}_{1}}\] and \[{{R}_{2}}\] are in parallel combination. |
Hence, equivalent resistance between A and C will be. |
\[\therefore \] \[{{R}_{eq}}=\frac{{{R}_{1}}{{R}_{2}}}{{{R}_{1}}+{{R}_{2}}}=\frac{4{{R}^{2}}}{4R}=R\] |
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