Current Electricity Charging Discharging Of Capacitors Question 737
Question: The charge flowing through a resistance R varies with time t as $ Q=at-bt^{2}. $ The total heat produced in R by the time current ceases is
Options:
A) $ a^{3}R/6b $
B) $ a^{3}R/3b $
C) $ \frac{a^{3}R}{2b} $
D) $ \frac{a^{3}R}{b} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ Q=at-bt^{2}\text{ }i=\frac{dQ}{dt}=a-2bt $
$ i=0\text{ for }t=t _{0}=a/2b,\text{ i}\text{.e}\text{.,} $ current flow from The heat produced= $ \int\limits _{0}^{t _{0}}{i^{2},R,dt.} $ Putting the value of I we get heat produced $ =\frac{a^{3}R}{6b}. $
BETA
