In the figure below, suppose the switch has been closed for a time interval suff
ID: 1778207 • Letter: I
Question
In the figure below, suppose the switch has been closed for a time interval sufficiently long for the capacitor to become fully charged. (Assume R1 = 15.0 k, R2 = 19.0 k, R3 = 6.00 k, and C = 13.0 F.)
(a) Find the steady-state current in each resistor.
I1 = A
I2 = A
I3 = A
(b) Find the charge Qmax on the capacitor.
C
(c) The switch is now opened at t = 0. Write an equation for the current in R2 as a function of time. (Use the following as necessary: t. Do not enter units in your answers. Assume the current is in microamperes, and t is in seconds.)
IR2 =
(d) Find the time interval required for the charge on the capacitor to fall to one-fifth its initial value.
ms
Explanation / Answer
a)
i1 = i2 = V/(R1 + R2) = 9 /(15 + 19) = 265 uA
i3 = 0 since capacitor is fully charge in steady state. hence no current flow in R3
b)
V2 = Voltage across R2 = Voltage across capacitor = i2 R2 = (265 x 10-6) (19 x 103) = 5.04 Volts
Q = C V2 = (13 x 10-6) (5.04) = 65.5 uC