Relationship Between Different Capacitors for Different Applied Voltages

In summary, the necessary relationship between the capacitances of the four capacitors is that C1/C2 = C3/C4, in order for no voltage difference to be set up between terminals c and d when a voltage is applied across terminals a and b. This arrangement would also work for the case of a voltage applied to terminals c and d, as long as the same relationship between capacitances is maintained.
  • #1
malindenmoyer
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In the arrangement shown, find the necessary relationship between the capacitances of the four capacitors in order that when a voltage is applied across terminals a and b, no voltage difference is set up between terminals c and d. Would this arrangement work for the case of the voltage applied to terminals c and d to give no voltage across a and b?

http://malindenmoyer.com/fig.gif

I am rather confused as the concept was just introduced to me, so any help and guidance would be appreciated.
 
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  • #2
C1 an C2 are connected in series. They carry the same charge q.
C3 and C4 are also connected in series, they both carry the charge Q.

The voltage across the capacitor C1 is Vac=Q1/C1=q/C1.
The voltage across the capacitor C2 is Vcb=q/C2.

The same holds for capacitors C3 and C4: Vad=Q/C3, Vdb=Q/C4

No voltage between c and d means that Vac=Vad and Vcb=Vdb.

Write down the equations for the voltages and eliminate the charges.

ehild
 

FAQ: Relationship Between Different Capacitors for Different Applied Voltages

What is the relationship between different capacitors for different applied voltages?

The relationship between different capacitors for different applied voltages is known as the capacitance. Capacitance is a measure of a capacitor's ability to store an electric charge. It is directly proportional to the applied voltage and inversely proportional to the distance between the plates of the capacitor.

How does the capacitance change with different applied voltages?

The capacitance increases with increasing applied voltage. This is because a higher voltage creates a stronger electric field between the plates of the capacitor, which allows it to hold more charge. Conversely, a lower applied voltage results in a weaker electric field and a lower capacitance.

Can capacitors with different capacitance values be used together in a circuit?

Yes, capacitors with different capacitance values can be used together in a circuit. However, they must be connected in series or parallel depending on the desired outcome. When connected in series, the total capacitance is reduced, while when connected in parallel, the total capacitance is increased.

How does the size and material of a capacitor affect its capacitance?

The size and material of a capacitor can have a significant impact on its capacitance. Generally, a larger capacitor will have a higher capacitance than a smaller one, as it has a larger surface area for charge storage. The material also plays a role, as some materials have a higher dielectric constant, making them more efficient at storing charge and resulting in a higher capacitance.

Can the voltage applied to a capacitor ever exceed its maximum rating?

No, the voltage applied to a capacitor should never exceed its maximum rating. Doing so can cause the capacitor to fail, potentially leading to injury or damage to the circuit. It is important to carefully select a capacitor with a voltage rating that can handle the expected voltage in the circuit.

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