Current Electricity 4 Question 31
31. A thin uniform wire $A B$ of length $1 m$, an unknown resistance $X$ and a resistance of $12 \Omega$ are connected by thick conducting strips, as shown in the figure. A battery and galvanometer (with a sliding jockey connected to it are also available). Connections are to be made to measure the unknown resistance $X$ using the principle of Wheatstone bridge. Answer the following questions. (2002, 5M)
(a) Are there positive and negative terminals on the galvanometer?
(b) Copy the figure in your answer book and show the battery and the galvanometer (with jockey) connected at appropriate points.
(c) After appropriate connections are made, it is found that no deflection takes place in the galvanometer when the sliding jockey touches the wire at a distance of $60 cm$ from $A$. Obtain the value of the resistance $X$.
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Solution:
- (a) There are no positive and negative terminals on the galvanometer because only zero deflection is needed.
(b)
(c)
$$ \begin{aligned} A J & =60 cm \\ \therefore \quad B J & =40 cm \end{aligned} $$
If no deflection is taking place. Then, the Wheatstone’s bridge is said to be balanced.
$$ \begin{array}{rlrl} \text { Hence, } & & \frac{X}{12} & =\frac{R _{B J}}{R _{A J}} \\ \text { or } & & \frac{X}{12} & =\frac{40}{60}=\frac{2}{3} \\ \text { or } & x & =8 \Omega \end{array} $$
