Quick capacitor image question

In summary, The equivalent capacitance of this set of capacitors is C1 + (C2 x C3)/(C2 + C3) = 10C/6.
  • #1
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Quick capacitor question

Homework Statement


Three capacitors are connected to a battery as shown in the figure below. Their capacitances are C1 = 3C, C2 = C, and C3 = 5C
p20-44.gif

What is the equivalent capacitance of this set of capacitors (in terms of C)?

Homework Equations


In parallel, Ctot=C1+C2+...+Cn
In series, 1/Ctot=1/C1+1/C2+...+1/Cn


The Attempt at a Solution


my book never says how to add capacitors that are both in series and parallel, so i have no idea. i know the formulas above, but idk how to combine them...
 
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  • #2
Do it in two parts.Use your first equation above -this gives you the single capacitor that can replace C2 and C3 and now you are left with this single capacitor in series with C1
 
  • #3


As a scientist, it is important to have a strong understanding of basic principles and equations in order to approach new problems. In this case, we can use a combination of the parallel and series equations to determine the equivalent capacitance of the set of capacitors.

First, we can see that C1 and C2 are connected in parallel, so we can use the equation Ctot = C1 + C2 to find the equivalent capacitance of these two capacitors. This gives us Ctot = 3C + C = 4C.

Next, we can see that C3 is connected in series with the combination of C1 and C2, so we can use the equation 1/Ctot = 1/C1 + 1/C2 + 1/C3 to find the total inverse capacitance. Substituting in the values from before, we get 1/Ctot = 1/4C + 1/5C, which simplifies to 9/20C.

Finally, we can take the inverse of this value to find the equivalent capacitance: Ctot = 20/9C.

In summary, the equivalent capacitance of this set of capacitors is 20/9 times the value of one of the individual capacitors (C). This approach can be used for any combination of capacitors in a circuit, as long as we understand the principles of parallel and series connections.
 

Related to Quick capacitor image question

1. What is a quick capacitor image?

A quick capacitor image is a representation or visual depiction of a capacitor, a passive electronic component used to store electrical energy in an electric field. It typically consists of two conductive plates separated by a dielectric material and is commonly used in electronic circuits.

2. How does a capacitor work?

A capacitor works by storing electrical energy in an electric field. When a voltage is applied to the capacitor, one plate becomes positively charged while the other becomes negatively charged. This creates an electric field between the plates, which stores the energy. When the capacitor is connected in a circuit, it can release this stored energy to perform various functions.

3. What are the different types of capacitors?

There are various types of capacitors, including ceramic, electrolytic, film, and variable capacitors. Ceramic capacitors are made of ceramic materials and are most commonly used in electronic circuits. Electrolytic capacitors are polarized and have higher capacitance values. Film capacitors are made of plastic film and are known for their stability and accuracy. Variable capacitors have a variable capacitance and are often used in tuning circuits.

4. How is the capacitance of a capacitor determined?

The capacitance of a capacitor is determined by the surface area of the plates, the distance between the plates, and the type of dielectric material used. The larger the surface area and the smaller the distance between the plates, the higher the capacitance. Different dielectric materials have different permittivity values, which also affect the capacitance of a capacitor.

5. What is the purpose of a capacitor in a circuit?

The purpose of a capacitor in a circuit is to store and release electrical energy as needed. It can also filter out unwanted signals or provide a temporary power supply during voltage fluctuations. Capacitors are also used in timing circuits, noise reduction, and power factor correction.

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