Current Electricity - Result Question 65
70. Ten identical cells connected in series are needed to heat a wire of length one meter and radius ’ $r$ ’ by $10^{\circ} C$ 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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======= ####70. Ten identical cells connected in series are needed to heat a wire of length one meter and radius ’ $r$ ’ by $10^{\circ} C$ 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 ’ $t$ ‘?
c3eec34ec6b1fad69db54a20ad4b2dca40c2aa54 (a) 10
(b) 20
(c) 30
(d) 40
[NEET Kar. 2013]
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Answer:
Correct Answer: 70. (b)
Solution:
- (b) Resistance is directly proportionl to length of the wire. As length is doubled so mass is doubled and resistance is doubled.
We have
$\frac{(10 E)^{2}}{R} t=m S \Delta T$, Now $\frac{(n E)^{2} t}{2 R}=(2 m) S \Delta T$
$\Rightarrow \frac{n^{2} E^{2} t}{2 R}=2 \frac{10^{2} E^{2} t}{R}$
$\Rightarrow n=20$
