For the LR circuit shown below, suppose the battery were replaced with a differe
ID: 1290970 • Letter: F
Question
For the LR circuit shown below, suppose the battery were replaced with a different battery having a voltage one half as much as that of the original battery. When the switch is closed, the time it takes for the current to reach half of its initial value is
longer than the time it took with the original battery.
shorter than the time it took with the original battery.
equal to the time it took with the original battery.
longer than the time it took with the original battery.
shorter than the time it took with the original battery.
equal to the time it took with the original battery.
For the LR circuit shown below, suppose the battery were replaced with a different battery having a voltage one half as much as that of the original battery. When the switch is closed, the time it takes for the current to reach half of its initial value is longer than the time it took with the original battery. shorter than the time it took with the original battery. equal to the time it took with the original battery.Explanation / Answer
equal to the time it took with the original battery.
the equation of current in LR circuit is I=Ii(e-(r/L)t)
time for 1st case
.5*Ii=Ii(e-(r/L)t)
(r/L)t=-1*ln(.5)
t=(-L*ln(0.5))/r
this time will be same for second case also because there is no change in R & L values. The initial current will increase in second case, but time to reach to half its initial value will be same.
so the answer is equal to the time it took with the original battery