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________.

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