Homelw6 In the circuit of the figure below, the switch S has been open for a lon

Question

Homelw6 In the circuit of the figure below, the switch S has been open for a long time. It is then suddenly closed. Take &10.0 V,R8.0 kn, 20o kn, and c 13.0 (a) Determine the time constant before the switch is closed (b) Determine the time constant after the switch is closed. rent in the switch as a function of time. (Assume is in A and t is in s. Do not enter units in your expression. Use the rent n the switch as a treton of tme. (Assume 1 is n A and t s n s. Do not enter units n your egresson. Use the (c) Let the switch be closed atto. Determine the cu following as necessary: t.) Need Help? 12. 12/12 points 1 Preious Answers

Explanation / Answer

Here,

a)
before closing the switch

for the time contant

T = (R1 + R2) * C

T = (48 *10^3+ 200*10^3) * 13 *10^-6 s

T = 3.224 s

the time contant of the circuit is 3.224 s

b)after closing the switch

for the time contant

T = R2 * C

T = 200*10^3 * 13 *10^-6 s

T = 2.6 s

the time contant of the circuit is 2.6 s

b)

for the function of current

I = Io * e^(-t/T)

I = (10/(200*10^3)) * e^(-t/2.6)

I = 5 *10^-5 * e^(-0.385 * t)

the current in the switch will be 5 *10^-5 * e^(-0.385 * t) A

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