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MHT CET 2024 (9 May, Shift 1) · Wheatstone Bridge & Metre Bridge

Wheatstone Bridge & Metre Bridge question from MHT CET 2024 (9 May, Shift 1)

Q31MHT CET 2024 · 9 MAY · SHIFT 1Medium

Wheatstone Bridge & Metre Bridge

When the two known resistances ' RR ' and ' SS ' are connected in the left and right gaps of a meter bridge respectively, the null point is found at a distance ' l1l_1 ' from the zero end of a meter bridge wire. An unknown resistance ' X ' is now connected in parallel with ' S ' and null point is found at a distance ' l2l_2 ' from zero end of meter bridge wire. The unknown resistance ' X ' is

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Answer: (a)

  1. RS=l1100−l1\dfrac{R}{S} = \dfrac{l_1}{100 - l_1} and R(S+X)SX=l2100−l2\dfrac{R(S+X)}{SX} = \dfrac{l_2}{100 - l_2}
  2. Divide: S+XX=l2(100−l1)l1(100−l2)\dfrac{S+X}{X} = \dfrac{l_2(100 - l_1)}{l_1(100 - l_2)}
  3. SX=l2(100−l1)−l1(100−l2)l1(100−l2)=100(l2−l1)l1(100−l2)\dfrac{S}{X} = \dfrac{l_2(100-l_1) - l_1(100-l_2)}{l_1(100-l_2)} = \dfrac{100(l_2 - l_1)}{l_1(100 - l_2)}
  4. X=Sl1(100−l2)100(l2−l1)X = \dfrac{S l_1 (100 - l_2)}{100(l_2 - l_1)}
  5. So the answer is (a).
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