Current Electricity Charging Discharging Of Capacitors Question 673
Question: The temperature coefficient of resistance of conductor varies as $ \alpha (T)=3T^{2}+2T $ . If $ R _{0} $ is resistance at T= 0 and R is resistance at T, then
Options:
A) $ R=R _{0}(6T+2) $
B) $ R=2R _{0}(3+2T) $
C) $ R=R _{0}(1+T^{2}+T^{3}) $
D) $ R=R _{0}(1-T+T^{2}+T^{3}) $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] $ \alpha (T)=\frac{1}{R _{0}}\frac{dR}{dT} $ or $ (3T^{2}+2T)=\frac{1}{R _{0}}\frac{dR}{dT} $ Or $ dR=R _{0}(3T^{2}+2T)dT $ Or $ \int\limits _{R _{0}}^{R}{dR=R _{0}[ 3\int\limits _{0}^{T}{T^{2}dT+2\int\limits _{0}^{T}{TdT}} ]} $ Or $ R=R _{0}[1+T^{2}+T^{3}] $
BETA
