Question 174: Current Electricity

Question

In a meter bridge experiment S is a standard
resistance. R is a resistance wire. It is found
that balancing length is $l$ = 25 cm. If R is
replaced by a wire of half length and half
diameter that of R of same material, then the
balancing distance $l'$ (in cm) will now
be________.
![](https://imagex.cdn.examgoal.net/7k9k2k5ldsw92/c928a6f4-ef71-4017-a3d5-01e3d649b90d/59191e60-3aed-11ea-92dd-4b9c3519996f/file-7k9k2k5ldsw93-448w.jpg)

Accepted Answer

${S \over R} = {{75} \over {25}}$ = 3
R = ${{\rho L} \over A}$ = ${{4\rho L} \over {\pi {d^2}}}$
R' = ${{4\rho \left( {{L \over 2}} \right)} \over {\pi {{\left( {{d \over 2}} \right)}^2}}}$ = 2R
Then ${S \over {R'}} = {{100 - l} \over l}$
$ \Rightarrow $ ${{100 - l} \over l}$ = ${S \over {2R}}$ = ${3 \over 2}$
$ \Rightarrow $ $l$ = 40 cm

Current Electricity

In a meter bridge experiment S is a standard resistance. R is a resistance wire. It is found that balancing length is l = 25 cm. If R is replaced by a wire of half length and half diameter that of R of same material, then the balancing distance l' (in cm) will now be________.

Integer / Numeric Answer Type