Halliday Chapter 25: Final Charge of Uncharged Capacitors Problem

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In summary, the conversation discusses a problem involving a 12 V battery and three uncharged capacitors of different capacitances. The switch is thrown to charge one capacitor and then switched to charge the other two in series. The final charges of each capacitor are calculated using equations, but the result does not match the answer in the book. The conversation then explores possible mistakes in the calculations and discusses the concept of shared charge in the system.
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george2
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Hi! I need help with the following problem:
1. Figure displays a 12 V battery and three uncharged capacitors of capacitances C1=4μF , C2=6μF and C3=3μF. The switch is thrown to the left until C1 is fully charged then it is thrown to the right.What is the final charge of each capacitor?


3. initial charge of 1 is q=C1V=48μC
Switch thrown to the right:
q2=q3, V1=V2+V3, V=q/c and q1+q2+q3=48C
From these equations i found q1=24,q2=q3=12
The answer in the back of the book says that q1=32,q2=q3=16
Where is the mistake?
 

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  • #2
Welcome to PF.

First of all figure the equivalent capacitance of the 2 capacitors in series.

Second figure the charge Q that will be imparted to the first capacitor C1.

You did this and got 48 from Q = V*C.

But when the switch is broken from the source, that then is your total charge that can be shared in the system.

When you connect the switch to the right you are now sharing that charge between C1 and the C2 and C3 equivalent.

Using Q = V*C , figure then the new voltage across the three.

With the resulting voltage you are in a position to determine the Q on C1 and the Q on the equivalent of C2 and C3.
 
  • #3
Now i find that: q1=32μC, q2=16μC, q3=16 μC.The sum of the 3 charges is 64 μC but there are only 48μC to share.Why does this happen?

P.S. Thank you for your help!
 

Related to Halliday Chapter 25: Final Charge of Uncharged Capacitors Problem

1. What is the purpose of Halliday Chapter 25?

Halliday Chapter 25 focuses on the final charge of uncharged capacitors, which is an important concept in understanding the behavior of capacitors in electrical circuits.

2. What is a capacitor?

A capacitor is an electrical component that stores energy in an electric field. It is made up of two conductive plates separated by an insulating material, called a dielectric.

3. What is the final charge of an uncharged capacitor?

The final charge of an uncharged capacitor is the amount of charge that is stored on the plates of the capacitor once it has reached its maximum charge capacity. This is determined by the capacitance of the capacitor and the voltage applied to it.

4. How is the final charge of an uncharged capacitor calculated?

The final charge of an uncharged capacitor can be calculated using the formula Q = CV, where Q is the charge in coulombs, C is the capacitance in farads, and V is the voltage applied to the capacitor. This formula assumes ideal conditions and does not take into account any losses in the circuit.

5. Why is understanding the final charge of uncharged capacitors important?

Understanding the final charge of uncharged capacitors is important in designing and analyzing electrical circuits. It allows us to predict the behavior of capacitors in circuits and ensure that they are functioning properly. It also helps us to determine the energy stored in a capacitor, which can be useful in various applications such as power supplies and energy storage systems.

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