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CBSE Class 12-science Answered

In the balanced wheat stone bridge current between a and b will be zero if  A) x/y = c1/c2  B) x/y = c2/c1
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Asked by prakriti12oct | 09 Aug, 2019, 12:16: AM
answered-by-expert Expert Answer
Capacitor A of capacitance C1 and capacitor B of capacitance C2 are connected in series bewteen points c and d.
 
Hence the charge q on capacitor plates are same for both the capacitors.
 
Let VA be the potential difference between c and a . Let VB be the potential difference between a and d
 
then we have,  begin mathsize 12px style fraction numerator V subscript B over denominator V subscript A plus V subscript B end fraction space equals space fraction numerator begin display style bevelled q over C subscript 2 end style over denominator begin display style bevelled q over C subscript 1 space plus space bevelled q over C subscript 2 end style end fraction space equals space fraction numerator C subscript 1 over denominator C subscript 1 plus C subscript 2 end fraction space equals space fraction numerator 1 over denominator 1 plus begin display style C subscript 2 over C subscript 1 end style end fraction end style  .......................(1)
Similarly for resistors X and Y connected in seriesbetween c and d ,
we can write, begin mathsize 12px style fraction numerator V subscript Y over denominator V subscript X plus V subscript Y end fraction space equals space fraction numerator y over denominator x plus y end fraction space equals space fraction numerator 1 over denominator 1 plus begin display style x over y end style end fraction space................... left parenthesis 2 right parenthesis end style
By comparing eqn.(1) and eqn.(2),  we have,  x/y  = C2/C1
Answered by Thiyagarajan K | 09 Aug, 2019, 12:47: PM

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