27.6.3. Consider the RC-circuit shown to the right. Initially switch S has been

Question

27.6.3. Consider the RC-circuit shown to the right. Initially switch S has been open for a long time. (a)
What is the charge on the capacitor when the switch SW has been open for a long time? (b) Next the
switch S is closed for a long time. What is the charge on the capacitor after the switch SW has been
closed for a long time?

the figure is a three branch circuit, the left branch consists of a 2 ohm resistor and a 2 volt battery, the middle branch is a 20uF capacitor, and the right branch consists of a 3 volt battery and a four ohm resistor. The swith is located in the top branch between the left and middle branch.

Explanation / Answer

a)

there is not any current in the circuit.

Q = C V = 20e-6 * 3 = 6e-5 C

b)

any current does not go through capacitor but we have a current goes through other resistors:

3 - 4 i - 2 - 2 i = 0

i = 1/6 = 0.16667 A

V = 3 - 4 i = 3 - 4 * 0.16667 = 2.333

Q = CV = 20e-6 * 2.333 = 4.67e-5 C

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