Question 639: Current Electricity

Question

Ten identical cells connected in series are needed to heat a wire of length one meter and radius 'r' by 10
o
C 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 10 o C 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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