Consider a capacitor with capacitance, C, where vC(t) is the voltage across the capacitor, and iC(t) is the current through the capacitor. (The polarity of vC(t) is chosen consistent with the passive sign convention.)
Assume :
vC(t) = 0 V, for t < 0- seconds and
vC(t) = 1 - e-5t volts for t > 0+.
1. Which, if any, of the following are true?
1-The current, iC(t), will start at zero, jump to some negative value, then increase to zero.
2-The current, iC(t), stays zero for all t.
3-The current, iC(t), will reach some positive constant value after a long time.
4-The current, iC(t), will start at zero, jump to some positive value, then decrease to zero.
5-The current, iC(t), will start at zero, gradually rise to some positive value, then decrease again to zero.
6- None of these.
7-The current, iC(t), will start at zero, gradually fall to some negative value, then increase again to zero.
8-The current, iC(t), is zero before t = 0.
9-The current, iC(t), will reach some negative constant value after a long time.
2. If C= 13 microfarads, find the value of the current, iC, through the capacitor at t = 0.27 seconds.
In microamperes.
3. Given the same capacitor, if
iC(t) = 0 amperes and vC(t) = 0 volts for t < 0- and
iC(t) = 20 e-3t amperes for t > 0+,
which, if any, of the following are true?
1-The voltage across the capacitor, vc(t), stays zero for all time.
2-The voltage across the capacitor, vc(t), will reach some positive constant value after a long time.
3- None of these choices.
4-The voltage across the capacitor, vc(t), will reach some negative constant value after a long time.
5-The voltage across the capacitor, vc(t), starts at zero, falls gradually to some negative value, then rises gradually to zero.
6-The voltage across the capacitor, vc(t), is zero before t = 0.
7-The voltage across the capacitor, vc(t), starts at zero, rises gradually to some positive value, then declines gradually to zero.
4. If the value of the capacitor is 39 microfarads, and if iC(t) is the same as in question 3 above, find the voltage across the capacitor at t = 7 seconds. In megavolts.