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Current Electricity

Question
CBSEENPH12039866

The resistances in the two arms of the meter bridge are 5 ohm and R ohm, respectively. When the resistance  R is shunted with an equal resistance, the new balance point is at 1.6 l1. The resistance R is,

  • 10 ohm

  • 15 ohm

  • 20 ohm

  • 25 ohm

Solution

B.

15 ohm

Case 1:
5 over straight l subscript 1 space equals space fraction numerator R over denominator left parenthesis 100 space minus space l subscript 1 right parenthesis end fraction       ... (i)
Now, by shunting resistance R by an equal resistance R, new resistance in that arm become R/2
So, fraction numerator 5 over denominator 1.6 space straight l subscript 1 end fraction space equals space fraction numerator begin display style bevelled R over 2 end style over denominator left parenthesis 100 space minus space 1.6 space l subscript 1 right parenthesis end fraction      ... (ii)
From equations (i) and (ii),
fraction numerator 1.6 over denominator 1 end fraction equals fraction numerator left parenthesis 100 space minus space 1.6 space l subscript 1 right parenthesis over denominator 100 space minus space l subscript 1 end fraction x 2
rightwards double arrow 160 - 1.6 l1 = 200 - 3.2 l1
            1.6 l1 = 40
               straight l subscript 1 space equals space fraction numerator 400 over denominator 1.6 end fraction equals 25 space straight m
From equation (i),
space space space space space 5 over 25 equals R over 75
rightwards double arrow space R space equals space 15 space capital omega

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