In the circuit of the figure below, the switch S has been open for a long time.

Question

In the circuit of the figure below, the switch S has been open for a long time. It is then suddenly closed. Take e m f = 10.0 V, R1 = 40.0 k?, R2 = 110 k?, and C = 15.0 ?F.

(a) Determine the time constant before the switch is closed.___s


(b) Determine the time constant after the switch is closed.___s

(c) Let the switch be closed at t = 0. Determine the current in the switch as a function of time. (Assume I is in A and t is in s. Do not enter units in your expression. Use the following as necessary: t.)
I = ___

Explanation / Answer

Emf = 10 volt

R1 = 40 k ohm = 40000 ohm

R2 = 110 k o ohm = 110,000 ohm

C= 15 micro F = 15×10-6 F

(a). For calculating the time constant , we just remove the battery and repkace it by wire .

Now equivalent resistance = R1 + R2 = 40000 + 110000 = 150,000 ohm

Time constant = equivalent resistance × capacitance = = 150,000 × (15×10-6) = 2.25 seconds

(b). After the switch is closed

Equivalent resistance across the capacitor = R2 = 110,000 ohm

Time constant = 110,000×(15×10-6) = 1.65 seconds.

(c). Current I = Io(e(-t/1.65)) A

Where Io = (1/1100) A

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