Question 668: Current Electricity

Question

Ten identical cells connected in series are needed to heat a wire of length one meter and radius 'r' by 10oC in time 't'. How many cells will be required to heat the wire of length two meter of the same radius by the same temperature in time 't' ?

Accepted Answer

Let $$ho $$ be resistivity of the material of the wire and r be radius of the wire.
Therefore, resistance of 1 m wire is
$$R = {{ho \left( 1 ight)} \over {\pi {r^2}}} = {ho  \over {\pi {r^2}}}$$
$$\left(\because {R = {{ho l} \over A}} ight)$$
Let $$\varepsilon $$ be emf of each cell. In first case,
10 cells each of emf $$\varepsilon $$ are connected in series to heat the wire of length 1 m by $$\Delta $$T(= 10ÃÂ°C) in time t.
$$ 	herefore {{\left( {10\varepsilon } ight)} \over R}r = ms\Delta T$$    ...(i)
In second case,
Resistance of same wire of length 2 m is
$$R' = {{ho \left( 2 ight)} \over {\pi {r^2}}} = {{2ho } \over {\pi {r^2}}} = 2R$$
Let n cells each of emf $$\varepsilon $$ are connected in series to heat the same wire of length 2 m, by the same temperature $$\Delta $$T (= 10ÃÂ°C) in the same time t.
$$ 	herefore {{{{\left( {n\varepsilon } ight)}^2}t} \over {2R}} = \left( {2m} ight)s\Delta T$$    ...(ii)
Divide (ii) by (i), we get
$${{{n^2}} \over {200}} = 2 \Rightarrow {n^2} = 400$$
$$ 	herefore $$ n = 20

Answer

20

Answer

30

Answer

40

Answer

10

Current Electricity

Ten identical cells connected in series are needed to heat a wire of length one meter and radius 'r' by 10oC in time 't'. How many cells will be required to heat the wire of length two meter of the same radius by the same temperature in time 't' ?

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