A current impulse 5δ(t) is forced through a capacitor C. The voltage vc(t) across the capacitor is given bya.a. 5tb.c.d.
Question
A current impulse 5δ(t) is forced through a capacitor C. The voltage vc(t) across the capacitor is given by:
- a. 5t
- b.
- c.
- d.
Solution
It seems like there's some confusion with your question as it's not fully formed. However, I can tell you that the voltage across a capacitor, given a current impulse, can be found using the formula:
V(t) = 1/C ∫ i(t) dt
Where:
- V(t) is the voltage across the capacitor
- C is the capacitance of the capacitor
- i(t) is the current at time t
- ∫ i(t) dt is the integral of the current with respect to time
Given a current impulse i(t) = 5δ(t), where δ(t) is the Dirac delta function, the voltage across the capacitor would be:
V(t) = 1/C ∫ 5δ(t) dt
The integral of the Dirac delta function is a step function, so the result would be:
V(t) = 5/C for t > 0
This means that the voltage across the capacitor jumps to 5/C at the instant the current impulse is applied, and remains at that level for t > 0.
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