The values of the components in a simple series RC circuit containing a switch a
ID: 1875013 • Letter: T
Question
The values of the components in a simple series RC circuit containing a switch and an initially uncharged capacitor (see figure below) are C = 1.40 µF, R = 1.90 M, and e m f = 10.0 V.
(a) the charge on the capacitor...
...a long time after the switch is closed q = µC
...1.9 s after the switch is closed q = µC
(b) the current in the resistor...
...immediately after the switch is closed I0 = µA
...1.9 s after the switch is closed I = µA
... a long time after the switch is closed I = µA
(c) The rate at which energy, 1.9 s after the switch is closed, is...
...being dissipated in the resistor Presistor = µW
...being stored in the capacitor Pcapacitor = µW
...being delivered by the battery Pbattery = µW
C=Explanation / Answer
a)
T = time constant = RC = (1.90 x 106) (1.40 x 10-6) = 2.66 sec
q = charge stored by capacitor after long time = CV = 1.40 x 10 = 14 µC
q = charge at time 1.9 sec = q (1 - e-t/T) = (14) (1 - e-1.9/2.66) = 7.15 µC
b)
Io = V/R = 10/(1.9 x 106) = 5.3 x 10-6 A
I = ( Io/T) e-t/T = ((5.3 x 10-6)/2.66) e-1.9/2.66 = 9.8 x 10-7 A
at long time
I = 0
c)
in resistor , P = I2 R = (9.8 x 10-7)2 (1.9 x 106) = 3.7 Watt
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