Current Electricity Charging Discharging Of Capacitors Question 657
Question: A wire of cross-section area A, length $ L _{1} $ resistivity $ {\rho _{1}} $ and temperature coefficient of resistivity $ {\alpha _{1}} $ is connected in series to a second wire of length $ L _{2} $ resistivity $ {\rho _{2}} $ , temperature coefficient of resistivity $ {\alpha _{2}} $ and the same are A, so that wires carry same current. Total resistance R is independent of temperature for small temperature change if (Thermal expansion effect is negligible)
Options:
A) $ {\alpha _{1}}=,-{\alpha _{2}} $
B) $ {\rho _{1}}L _{1}{\alpha _{1}}+{\rho _{2}}L _{2}{\alpha _{2}}=0 $
C) $ L _{1}{\alpha _{1}}+L _{2}{\alpha _{2}}=0 $
D) None of these
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Answer:
Correct Answer: B
Solution:
[b] Let initial resistance of the wires are $ R _{1} $ and $ R _{2} $ respectively. Then $ R _{1}’+R{’ _{2}}=R _{1}+R _{2} $
$ \Rightarrow R _{1}(1+{\alpha _{1}}\Delta T)+R _{2}(1+{\alpha _{2}}\Delta T)=R _{1}+R _{2} $
$ \Rightarrow R _{1}a _{1}+R _{2}a _{2}=0 $
$ \Rightarrow \frac{{\rho _{1}}L _{1}}{A}{\alpha _{1}}+\frac{{\rho _{2}}L _{2}}{A}{\alpha _{2}}=0. $
$ \Rightarrow {\rho _{1}}L _{1}{\alpha _{1}}+{\rho _{2}}L _{2}{\alpha _{2}}=0 $ .
BETA
