In the circuit shown in the figure below, switch S has been open for a long time

Question

In the circuit shown in the figure below, switch S has been open for a long time. At time t = 0 the switch is then closed. (Let R1 = 188 ?, R2 = 660 ?, C = 4.55

In the circuit shown in the figure below, switch S has been open for a long time. At time t = 0 the switch is then closed. (Let R1 = 188 ?, R2 = 660 ?, C = 4.55 muF, and V = 55.0 V. Give your answers to 3 significant figures.) What is the battery current just after switch S is closed?I0 = A **Use Correct Sig Figs What is the battery current a long time after switch S is closed?I? = A **Use Correct Sig Figs What is the current in the resistor R2 = 660 ? as a function of time? (Use the following as necessary: t.) I2(t) = give priority to first correctly answered question. I can't give everyone the five stars for effort that I wish I could. Good luck

Explanation / Answer

a) just after closed R2 is shorted so R = r1

so I = 55/188= 0.293

b) after a long time no current flows through C so R = R1 + R2

I = 55/(188+660)=0.0649 A

c)

so we know I1 = IC + I2

V - I1 R1 - Q/C = 0

so I1 = (V- Q/C)/R1

and

Q/C - I2 R2 = 0

I2 = 1/R2 Q/C

and Ic = dQ/dt
so we have

(V-Q/C)/R1 = dQ/dt + 1/R2 Q/C

so
dQ/dt = V/R1 - 1/R1 Q/c -1/R2 Q/C

dQ/dt = 55/188 - Q/(188*4.55E-6) - Q/(660*4.55E-6)

Q = 1.948E-4 *(1 - e^(-1502.04 t))

so

I2 = 1.948E-4/(660*4.55E-6) *(1 - e^(-1502.04 t))

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