Score: 0 of 1 pt Score: 74 696, 15 67 of 21 Phys Sci 12.4.59 In a by dosing a sw

Question

Score: 0 of 1 pt Score: 74 696, 15 67 of 21 Phys Sci 12.4.59 In a by dosing a switch) is given by the equation Q()-CRC)), where C, V, and R are constants. Further, the instantaneous charging current I, is the rate of Ate change of charge on the capadifor, or leQ/dt Thi a. Find the expression tor ie as a tunction of time. b. It C-104farads. R-100 ohms, and V- 10 volts, what is the charging current ater 200 seconds? (Hiet When placed into the tfunction in part a the units can be combined into amps.) To see 1 OK

Explanation / Answer

a)

Q(t) =CV(1-e-t/(RC))

differentiate with respect to t

dQ/dt =CV(0- (e-t/(RC))*(-1/RC))

dQ/dt =CV(1/RC)e-t/(RC)

dQ/dt = (V/R)e-t/(RC)

Ic = (V/R)e-t/(RC)

b)

R=106, C=10-4F ,V=10 ,t=200

Ic = (10/106)e-200/(106*10-4)

Ic = (1/105)e-2

Ic = (1/(105e2))amps exactly

Ic = 0.00000135335 amps approximately

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