Finding Total Capacitance with Electrical Breakdown

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In summary, a potential difference of 100 V is applied across a capacitor arrangement with capacitances C1 = 13.0 µF, C2 = 6.76 µF, and C3 = 4.14 µF. When capacitor 3 undergoes electrical breakdown and becomes equivalent to conducting wire, the increase in (a) the charge in microcoulombs on capacitor 1 and (b) the potential difference across capacitor 1 can be determined by computing the total capacitance of C1 and C2 in parallel (3.42 µF) and dividing it by the initial charge on C1 (3.42e-4 C) for part (b). For part (a), the original value
  • #1
catie1981
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Homework Statement



In figure 25-29, a potential difference of V = 100 V is applied across a capacitor arrangement with capacitances C1 = 13.0 µF, C2 = 6.76 µF, and C3 = 4.14 µF. If capacitor 3 undergoes electrical breakdown so that it becomes equivalent to conducting wire, what is the increase in (a) the charge in microcoulombs on capacitor 1 and (b) the potential difference across capacitor 1?
http://img45.imageshack.us/img45/9895/fig2528iq2.gif


Homework Equations


series capacitance 1/Ctotal= 1/C1 + 1/C2 + 1/C3
parallel capacitance Ctotal = C1 + C2 + C3
q= CV

The Attempt at a Solution


well, I've tried many different ways- but I guess my biggest problem comes from not knowing whihc of the capacitors to add up first- meaning do I add together C1 and C2 first, or C2 and C3, or C1 and C3? If you add them up starting with those different pairs, the total capacitance comes to different values each time, so that could be a problem. After, that I might be abel to work it backwards to figure out the rest of the problem...I just can't get it off the ground...thanks
 
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  • #2
C1 and C2 form a parallel pair. Compute their total capacitance.

The parallel combination of c1 and c2 are in series with C3.
 
  • #3
uh-oh...ok so I have that C123=3.42microFarad, which will also give q123=3.42e-4C...since C3 will be essentially taken out of the equation, I would need to figure out what the new total capctitance is without c3, right? Or did I miss something?
 
  • #4
oooo, ok so I've got part (b)...which I got by simply dividing q123 by C12...however, how to get part (a)...that's the tricky part...I'm not really sure how to manipulate these numbers to determine q1 in the first place...
 
  • #5
OK, so I now know where I'm having trouble...I don't know what the ORIGINAL value for q1 is, so if anyone can point me in the right direction to determine q1 before, maybe I can do q1 after...thanks
 
  • #6
wooops, I got it solved...thanks anyway :)
 
  • #7


how did you solve this first one?
 

1. How do you calculate total capacitance in a series circuit?

In a series circuit, the total capacitance is calculated by adding up the individual capacitance values of each capacitor. This is because in a series circuit, the capacitors are connected end-to-end, so the same amount of charge passes through each capacitor. The formula for calculating total capacitance in a series circuit is: Ctotal = C1 + C2 + ... + Cn, where C represents capacitance.

2. What is the formula for calculating total capacitance in a parallel circuit?

In a parallel circuit, the total capacitance is calculated by adding up the reciprocals of the individual capacitance values and taking the reciprocal of the sum. This is because in a parallel circuit, the capacitors are connected side-by-side, so the voltage across each capacitor is the same. The formula for calculating total capacitance in a parallel circuit is: 1/Ctotal = 1/C1 + 1/C2 + ... + 1/Cn, where C represents capacitance.

3. How do you calculate total capacitance when the capacitors are in a combination of series and parallel?

In this case, you can use a combination of the two formulas mentioned above. First, calculate the total capacitance for the capacitors in series, and then use this value as one of the individual capacitance values in the formula for parallel circuits. Alternatively, you can use the equivalent capacitance formula, which takes into account the combination of series and parallel capacitors. The formula is: Ceq = C1 + C2 + ... + Cn, where C represents the equivalent capacitance value.

4. Is there a maximum limit for total capacitance in a circuit?

Yes, there is a maximum limit for total capacitance in a circuit. This limit is determined by the power source and the resistors in the circuit. If the total capacitance exceeds this limit, it can cause the circuit to malfunction or even damage the components. It is important to check the specifications of the power source and the resistors before calculating the total capacitance for a circuit.

5. How does the distance between capacitors affect the total capacitance?

The distance between capacitors does not have a direct effect on the total capacitance. However, it can indirectly affect the capacitance by changing the dielectric constant. The dielectric constant is a measure of the insulating ability of a material between two conductors, and it affects the capacitance of a capacitor. When the distance between capacitors is changed, the dielectric constant may also change, resulting in a change in the total capacitance.

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