The values of the components in a simple series RC circuit containing a switch a
ID: 1595363 • 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 mu F, R = 2.20 M Ohm, and epsilon = 10.0 V. (a) the charge on the capacitor... ...a long time after the switch is closed q_infinity muC ...3.9 s after the switch is closed Q = mu C (b) the current in the resistor... ...immediately after the switch is closed I_0 = mu A ...3.9 s after the switch is closed I = mu A ... a long time after the switch is closed L middot = mu A (c) The rate at which energy, 3.9 s after the switch is closed, is. ...being dissipated in the resistor = mu A ...being stored in the capacitor P_capacitor = mu W ...being delivered by the battery P_battery = mu WExplanation / Answer
R*C = 2.2*10^6*1.4*10^(-6) = 3.08 s
(a)
Qo = C*V = 1.4*10 = 14 uC
Q a long time after switch is closed,
Q = Qo = 14 uC
Q at 3.9 s,
Q = Qo*(1 - e^(-t/R*C))
Q = 14*(1 - e^(-3.9/3.08))
Q = -6.32 uC
(b)
current at t = 0,
l = 10 / 2.2*10^6 = 4.54 uA
voltage across capacitor at t = 3.9 s
V = Q / C = -6.32 / 1.4 = -4.51 V
current at t = 3.9 s
l = 10 + 4.51 / 2.2 = 6.59 uA
after long time, l = 0
(c)
Presiator at 3.9 s
Pr = 10 - (-4.51)*659 = 95.7 W
Pcapacitor = (1/2)*Q*V = (1/2)*6.32*4.51
Pc = 14.25 W
Pbattery = 10*6.59 = 65.9*10^(-6) W
answer
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