How Do You Calculate Energy Stored in Specific Capacitors Within a Network?

In summary, we have a capacitor network with a potential difference of 12.0V across ab. Using the equations for calculating equivalent capacitance and energy stored in a capacitor, we can find that the total energy stored in the network is 1.58E-4 J. To find the energy stored in the 4.8μF capacitor, we first need to find the equivalent capacitance of the network. This is calculated to be 2.19E-6 F. Using the formula U = .5CV^2, where C is the capacitance and V is the potential difference, we can find that the energy stored in the 4.8μF capacitor is 3.46E-5 J.
  • #1
Gwozdzilla
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Homework Statement


For the capacitor network shown in Fig. P24.55, the potential difference across ab is 12.0V. Find (a) the total energy stored in this network and (b) the energy stored in the 4.80-μF capacitor.

Homework Equations


C= Q/V
U= Q2/2C = .5CV2 = .5QV
Capacitors in Series:
1/Ceq = 1/C1 + 1/C2 + ...
Capacitors in Parallel:
Ceq = C1 + C2 + ...

The Attempt at a Solution


I found part A:
C1 = 8.6E-6
C2 = 4.8E-6
Capacitors in Series:
1/Ceq = 1/C1 + 1/C2 + ...
1/Ceq = 1/(8.6E-6) + 1/(4.8E-6)
Ceq = 3.08E-6

C1 = 6.2E-6
C2 = 11.8E-6
Capacitors in Series:
1/Ceq = 1/C1 + 1/C2 + ...
1/Ceq = 1/(6.2E-6) + 1/(11.8E-6)
Ceq = 4.06E-6

C = 3.5E-6
Capacitors in Parallel:
Ceq = C1 + C2 + ...
Ceq = 3.5E-6 + 4.06E-6
Ceq = 7.56E-6

Capacitors in Series:
1/Ceq = 1/C1 + 1/C2 + ...
1/Ceq = 1/(7.56E-6) + 1/(3.08E-6)
Ceq = 2.19E-6

U = .5CV2
U = .5(2.19E-6)(122)
U = 1.58E-4 J

But then for part B I'm not really sure what to do. The voltage for the entire network is 12V, but I have no idea how I can use this info to find the potential energy for just one of the capacitors. Please help.
 

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  • #2
Determine the charge stored in the equivalent capacitor. How is it related to the charge of the 4.8μF capacitor?


ehild
 

1. What is a capacitor in a network?

A capacitor in a network is an electronic component that stores and releases electrical energy. It is made up of two conductive plates separated by an insulating material, and it is used to block or allow the flow of electrical current in a circuit.

2. How does a capacitor affect a network?

A capacitor can affect a network in different ways depending on its placement and value. In series, it can block DC current and allow AC current to pass through. In parallel, it can store and release energy, stabilize voltage and filter out noise from a circuit.

3. What are the types of capacitors used in a network?

The most commonly used capacitors in a network are ceramic, electrolytic, and film capacitors. Ceramic capacitors are compact and have a wide range of capacitance values. Electrolytic capacitors have a higher capacitance value and are used for filtering and power supply applications. Film capacitors have excellent stability and low leakage, making them suitable for high-frequency circuits.

4. What is the role of capacitors in a power supply network?

In a power supply network, capacitors are used to filter out AC ripple and provide stable DC voltage. They also help to regulate the voltage and protect sensitive components from voltage spikes. In some cases, capacitors are used to store energy and provide backup power in case of a power failure.

5. How do you calculate the capacitance required for a network?

The capacitance required for a network depends on the specific application and circuit design. It can be calculated using the formula C = Q/V, where C is the capacitance in Farads, Q is the amount of charge required, and V is the voltage. It is also important to consider other factors such as frequency, temperature, and tolerance when selecting a capacitor for a network.

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