Consider the circuit in the figure below, in which V = 24 V, and the switch has

Question

Consider the circuit in the figure below, in which V = 24 V, and the switch has been in position a for a long time. The switch is changed to position b at t = 0 s.

Which is true shortly after the switch is moved to position b?

a. The capacitor is charging

b. The capacitor is discharging
What is the voltage acaross the capacitor VC at the times tabulated below?

What are the charge Q on the capacitor and the current I through the resistor at the times tabulated below?
HINTS: Remember that C, Q, and VC are related when finding the charge on the capacitor. Then remember how VC and VR are related for the discharging capacitor. Finally, don't forget Ohm's law. This will allow you to find the current through the resistor.
Pay attention to the required units.

Explanation / Answer

When the switch is moved to b, the capacitor is discharging.

For a discharging capacitor, the voltage is given by:

V = Vo e-t/RC

so when the switch is immediately closed, t = 0s, therefore V = Vo = 24 volts

for this time the current will be: i = V/R = 24/50 = 480 mA

and Q = CV = 48uC

when t = 55us,

V = 24e-55u/RC = 13.847volts

for this time the current will be: i = 13.847/50 = 276.94 mA

and Q = CV = 27.694 uC

when t = 200us,

V = 24e-200u/RC = 3.248volts

for this time the current will be: i = 3.248/50 = 64.961 mA

and Q = CV = 6.496 uC.

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