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What is the voltage across a capacitor a...

What is the voltage across a capacitor at the time of switching, that is, when t=0?
a) Infinity
b) 0V
c) Cannot be determined
d) 1V

Text Solution

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a. The time takenby the car to cover 20 km before the turnis `(20 km)/(40 km/h)=1/2h`. The fly moves at a constant speed of 100 km/h during this time. Hence the total distance covred by it is `100 km/hxx1/2h=50 km`.
b. Suppose the car is at a distance dx away (at A) wqhen the fly is at teh wall (at O). The fly hits the glsspane at B, taking a time t. Then
b. Suppose the car is at a distasnce x away (at A) when the fly is at the wall (at O). The fly hits the glasspane at B, taking a time t. Then
`AB=(40 km/h)t`
and `OB=(100 km/h)t`
Thus, `x=AB+OB`
`=(140 km/h)t`
or, `t=x/(140 km/h) or OB = 5/7x`
. The fly returns to teh wall and during this period the car moves the distance BC. The time taken by the fly in this return path is
`((5x/7)/(100 km/h)=x/(140k/h)`
Thus, `BC=(40x)k/140 =2/7x`
or, `OC=OB-BC=3/7x`
IF at teh beginning opf the round trip (wall to the car and back) the car is a distance x away, it is `3/7x` away when the next trip again starts.
Distance of the car at the beginning of the 1st trip=20 km.
Distance of the car at the begining of the 2nd trip
`=3/7xx20 km`
Distance of the car at the beginning of the 3rd trip `(3/7)^2xx20km`,
Distance of the car at the beginning of the 4th trip
`=(3/7)^2xx20 km`
Distance of teh car at the begining of the nth trip
`=(3/7)^(n-1)xx20 km`
Trips will go on till the car reaches the turn the is the distance resuce of zero. This will be the case when n be comes infinity. Hence the fly makes an infinite number of tris before the car takes the turn.
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