Imagine that a capacitor of capacitance C is charged so that the potential diffe

Question

Imagine that a capacitor of capacitance C is charged so that the potential difference between its plates is V_0. At time t = 0, the capacitor is allowed to begin its discharge through a resistor of resistance R, as shown in fig 26-18 in our textbook. For questions 6 to 13, give all answers in terms of C, V_0, t and R only. What is the initial charge Q_0 of the capacitor, immediately before we start discharging it? (Only C and V_0 will appear in the answer.) What is the initial energy U stored the capacitor, immediately before we start discharging it? (Only C and V_0 will appear in the answer.) What is the time constant tau for the capacitor discharge? (Only C and R will appear in the answer.) Write out explicitly Q(t), the charge on the capacitor as it undergoes discharge. (Only C, t, R, and V0 will appear in the answer.)

Explanation / Answer

Here,

6) just after we start discharging the capacitor

as still all the charge is on the capacitor

Qo = C * Vo

7)

for the initial energy

initial energy stored = 0.5 * C * V^2

initial energy stored = 0.5 * C * Vo^2

8)

for the time constant

time constant , T = R * C

9)

for the charge on the capacitor

Q(t) = Qo * (e^(-t/T))

Q(t) = C * Vo * ( e^(-t/(R * C)))

the charge on capacitor while discharging is C * Vo * ( e^(-t/(R * C)))

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---