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Chapter 23: Problem 8

Does the capacitance describe the maximum amount of charge a capacitor can hold, in the same way that a bucket's capacity describes the maximum amount of water it can hold? Explain.

Short Answer

Expert verified
No, capacitance does not describe the maximum amount of charge a capacitor can hold like a bucket's capacity describes the maximum amount of water it can hold. If more charge is added after reaching its capacitance, the voltage across the capacitor will increase, but it will not 'overflow' with charge.

Step by step solution

01

Understanding the concept of capacitance

Capacitance is defined as the ratio of the change in electric charge of a system to the corresponding change in its electric potential. It is usually denoted by the symbol 'C' and measured in farads (F). Capacitance of a capacitor is given by the formula \( C= \frac{Q}{V} \) where Q is the charge and V is the voltage.
02

Understanding the metaphor of bucket's capacity

In the context of the bucket, capacity refers to the maximum amount of water it can hold before it overflows. If we go beyond this capacity, the water will spill or 'overflow'.
03

Relating capacitance to bucket concept

While both the bucket and the capacitor have a certain 'capacity', the concept differs slightly. In case of the bucket, once we reach its capacity, any additional water will overflow. However, in case of the capacitor, if we keep adding charge past its capacitance, it will increase the voltage across the capacitor rather than causing an 'overflow' of charge. Hence, capacitance does not define the maximum charge a capacitor can hold.
04

Final conclusion

After analyzing the concept of capacitance, it can be said that, unlike a bucket's capacity to hold water, capacitance does not describe the maximum amount of charge a capacitor can hold. Instead, the capacitance of a capacitor dictates how much voltage will result for a given amount of electric charge.

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Most popular questions from this chapter

(a) Write the electrostatic potential energy of a pair of oppositely charged, closely spaced parallel plates as a function of their separation \(x\), their area \(A\), and the charge magnitude \(Q\). (b) Differentiate with respect to \(x\) to find the magnitude of the attractive force between the plates. Why isn't the force equal to the charge on one plate times the electric field between the plates?

A capacitor is said to carry a charge \(Q .\) What's the net charge on the entire capacitor?

Show that the units of \(\epsilon_{0}\) may be written as \(\mathrm{F} / \mathrm{m}\)

Four 75 -\muC charges, initially far apart, are brought onto a line where they're spaced at 5.0 -cm intervals. How much work does it take to assemble this charge distribution?

A solid conducting slab is inserted between the plates of a capacitor, not touching either plate. Does the capacitance increase, decrease, or remain the same?
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