Current Electricity Charging Discharging Of Capacitors Question 156
Question: A wire of length L and 3 identical cells of negligible internal resistances are connected in series. Due to current, the temperature of the wire is raised by $ \Delta $ T in a time t. A number N of similar cells is now connected in series with a wire of the same material and cross’section but of length 2 L. The temperature of the wire is raised by the same amount $ \Delta $ T in the same time t. the value of N is
[IIT-JEE (Screening) 2001]
Options:
A) 4
B) 6
C) 8
D) 9
Show Answer
Answer:
Correct Answer: B
Solution:
Let R and m be the resistance and mass of the first wire, then the second wire has resistance 2R and mass 2m. Let E = emf of each cell, S = specific heat capacity of the material of the wire. For the first wire, current $ i _{1}=\frac{3E}{R} $ and $ i _{1}^{2}Rt=mS\Delta T $ For the second wire, $ i _{2}=\frac{NE}{2R} $ and $ i _{2}^{2}(2R)t=2mS\Delta T $ . Thus, $ i _{1}=i _{2} $ or $ N=6 $ .
BETA
