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CBSE Class 12 Physics 2017 Outside Delhi Set 1 Paper

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Question : 17 of 26
Marks: +1, -0
(a) Write the principle of working of a metre bridge.
(b) In a metre bridge, the balance point is found at a distance l1l_1 with resistances RR and SS as shown in the figure.
An unknown resistance XX is now connected in parallel to the resistance SS and the balance point is found at a distance l2l_2. Obtain a formula for XX in terms of l1,l2l_1, l_2 and SS.
Solution:  
(a) Principle of meter bridge
(b) Relation between l1,l2l_1, l_2 and SS
(a) The principle of working of a meter bridge is same as that of a balanced Wheatstone bridge.
(Alternatively:
When, ig=0i_g=0, then   PQ=  RS\;\frac{P}{Q}=\;\frac{R}{S}
(ii)   RS=  l1100−l1\;\frac{R}{S}=\;\frac{l_1}{100-l_1}
When XX is connected in parallel
  R(  XSX+S)=  l2100−l2\;\frac{R}{\left(\;\frac{X S}{X+S}\right)} = \;\frac{l_2}{100-l_2}
On solving, we get
X=  l1S(100−l2)100(l2−l1)X=\;\frac{l_1 S (100-l_2)}{100 (l_2-l_1)}
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