Current Electricity Charging Discharging Of Capacitors Question 151
Question: Two resistances $ R _{1} $ and $ R _{2} $ are made of different materials. The temperature coefficient of the material of $ R _{1} $ is $ \alpha $ and of the material of $ R _{2} $ is $ -\beta $ . The resistance of the series combination of $ R _{1} $ and $ R _{2} $ will not change with temperature, if $ R _{1}/R _{2} $ equals
[MP PMT 1997]
Options:
A) $ \frac{\alpha }{\beta } $
B) $ \frac{\alpha +\beta }{\alpha -\beta } $
C) $ \frac{{{\alpha }^{2}}+{{\beta }^{2}}}{\alpha \beta } $
D) $ \frac{\beta }{\alpha } $
Show Answer
Answer:
Correct Answer: D
Solution:
$ R _{1}+R _{2}=R _{1}(1+\alpha t)+R _{2}(1-\beta ,t) $
Therefore $ R _{1}+R _{2}=R _{1}+R _{2}+R _{1}\alpha t-R _{2}\beta t $
Therefore $ \frac{R _{1}}{R _{2}}=\frac{\beta }{\alpha } $
BETA
