Potential difference Capacitance problem

In summary, when the potential difference V = 100 V is applied to the capacitor arrangement shown in the figure, the increase in (a) the charge on capacitor 1, and (b) the potential difference across capacitor 1 is 39.5V.
  • #1
endeavor
176
0

Homework Statement


http://img509.imageshack.us/img509/8805/problem5fw8.th.png
The potential difference V = 100 V is applied to the capacitor arrangement shown in the figure. Here C1 = 10 microF, C2 = 5 microF, and C3 = 4microF. If capacitor C3 undergoes electrical breakdown (i.e. becomes equivalent to a conducting wire), what is the increase in (a) the charge on capacitor 1, and (b) the potential difference across capacitor 1?

The Attempt at a Solution


I wasn't sure how to solve it so I started doing different things:
I first found the equivalent capacitance, and with that I found the total charge to be Q_tot = 3.16 * 10^-4 C.
Then, I thought since the equivalent of C1 and C2, and C3 are in series, Q1 + Q2 = Q3, so Q_tot = 2 * Q3.
Then, from Q3 and C3, I find the potential difference across of C3 to be V3 = 39.5V, which in turn makes V1 = V2 = 60.5V.
From V1 and V2, I found the initial charges Q1 = 605 microC, and Q2 = 302.5 microC.
I'm not sure where to go from here...

I tried also to find the final potential difference across C1:
C12 = C1 + C2 = Q_tot / V_new
V_new = 21V, but it's supposed to be 79V... what am I doing wrong here?

Since Q = CV, if I plug in V = 79V, then Q1 = 790 microC, which is the answer for part (a), right? So should I try to solve part (b) first?

Any help would be greatly appreciated!

P.S. sorry for not using tex...
 
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  • #2
you've made a mistake

Q1 + Q2 = Q3, so Q_tot = 2 * Q3.

this is the faulty assumption

it should be
Q1 + Q2 = Q3 = Q_tot
 
  • #3
But if Q1 + Q2 = Q3, and Q_tot = Q1 + Q2 + Q3, then Q_tot = Q3 + Q3 = 2*Q3 ... right?
 
  • #4
endeavor said:
But if Q1 + Q2 = Q3, and Q_tot = Q1 + Q2 + Q3, then Q_tot = Q3 + Q3 = 2*Q3 ... right?

you just restated what i already said was wrong

Q_tot = Q1 + Q2 = Q3
 

Related to Potential difference Capacitance problem

1. What is potential difference?

Potential difference, also known as voltage, is the difference in electric potential energy between two points in an electric field. It is measured in volts (V) and represents the amount of work needed to move a unit of electric charge from one point to another.

2. What is capacitance?

Capacitance is the ability of a system to store electric charge. It is measured in farads (F) and is determined by the geometry and material properties of the system. In a capacitor, capacitance is directly proportional to the potential difference across it.

3. How do potential difference and capacitance affect each other?

Potential difference and capacitance are directly proportional to each other. This means that as the potential difference increases, the capacitance also increases. This relationship is described by the equation C = Q/V, where C is capacitance, Q is charge, and V is potential difference.

4. What is a potential difference capacitance problem?

A potential difference capacitance problem involves calculating the potential difference or capacitance in a system, given certain parameters or variables. These types of problems are common in physics and electrical engineering and require an understanding of the relationship between potential difference and capacitance.

5. How can potential difference and capacitance be used in practical applications?

Potential difference and capacitance have a wide range of practical applications, including in electronic circuits, power transmission, and energy storage. Capacitors, which utilize the relationship between potential difference and capacitance, are used in various devices such as computers, cameras, and radios. These concepts are also important in understanding the behavior of electricity in the human body and can help in the diagnosis and treatment of certain medical conditions.

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