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  • When two resistances X and Y are put in the left hand and right hand gaps in a wheatstone meter bridge, the null point is at 60cm. If X is shunted by a resistance equal to half of itself then find

When two resistances X and Y are put in the left hand and right hand gaps in a wheatstone meter bridge, the null point is at 60cm. If X is shunted by a resistance equal to half of itself then find the shift in the null point.

Option: 1

26.7 cm


Option: 2

36.7 cm


Option: 3

46.7 cm


Option: 4

96.7 cm


Answers (1)

best_answer

Arrangement is shown in the figure.
\frac{X}{Y}=\frac{60}{40}=\frac{3}{2} .....(1)
When X is shunted then resistance in the left gap becomes
X^{\prime}=\frac{X \cdot \frac{X}{2}}{X+\frac{X}{2}}=\frac{X}{3} ....(2)
\therefore\begin{aligned} & \text { Now } \frac{\left(\frac{\mathrm{X}}{3}\right)}{\mathrm{Y}}=\frac{l}{(100-l)} \Rightarrow \frac{1}{3} \times \frac{3}{2}=\frac{l}{(100-l)} \Rightarrow l=33.3 \mathrm{~cm} \\ & \text { Shift }=60-33.3=26.7 \mathrm{~cm} . \end{aligned}
    

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