AL phy capacitor

2009-08-13 5:07 am
In the circuit, the battery has a constant e.m.f. of 10V and negligible internal resistance. A 4 kilo-ohm resistor and a 2 micro-farad capacitor are connected in series with the battery. A 6 kilo-ohm resistor and a 2 micro-farad capacitor are connected in parallel across the ends of the 2 micro-farad capacitor mentioned before. In addition, a switch K is connected in parallel with the second 2 micro-farad capacitor.

Initially, switch K is closed. The switch K is then opened. What is the total additional charge given to the two capacitors when a steady state is reached ?

A. 8 micro-coulomb

B. 12 micro-coulomb

C. 28 micro-coulomb

D. 40 micro-coulomb
更新1:

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回答 (1)

2009-08-13 5:36 am
✔ 最佳答案
The answer is C.

Let's call the first capacitor be capacitor A (the one connected in series with the 4 kilo-ohm resistor), the second one be capacitor B.

Initially, K is closed, so capacitor B is shorted, and it does not have any charge on itself.

And at steady state, a capacitor acts as an open circuit.

So, the potential difference across capacitor A = potential difference across the 6 kilo-ohm resistor = 6 / (4 + 6) X 10 = 6 V

By Q = CV

Charge, Q = (2 X 10-6)(6) = 12 uC

Now, K is open, so the circuit is 'opened'. So, the two resistors can be ignored now.

It is in reality only two capacitors in parallel.

The equivalent capacitance = 2 + 2 = 4uF

And the potential difference = E.m.f. of the battery = 10 V

So, the number of charge on the capacitors, Q'

= C'V'

= (4 X 10-6)(10)

= 40 uC

Therefore, the additional number of charge

= Q' - Q

= 40 - 12

= 28 uC

參考: Physics king


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