Understanding Capacitance: A Simple Analogy for Beginners

When a 9.00 V battery is connected to the plates of a capacitor, it stores a charge of 27.0 μC. This problem can be broken down into two parts: determining the value of the capacitance and then finding the charge stored when the same capacitor is connected to a 12.0 V battery. Let's explore this concept step-by-step using an analogy.

What is Capacitance?

Capacitance is the ability of a capacitor to store an electric charge. It's a fundamental concept in physics and engineering, often represented by the symbol C. Capacitance is measured in farads (F).

Analogous to a Measuring Cup and Containers

To understand capacitance better, consider a measuring cup filled to 8 oz. Imagine a test tube that is 1 inch in diameter and long enough to hold that 8 oz. of liquid, and a pie pan that is 9 inches in diameter but also filled to 8 oz. Now, both containers have enough volume to hold the 8 oz. of liquid, but the test tube will show a higher water level compared to the pie pan. This difference in height can help us understand the capacity of each container.

In the context of electrical capacitance, the height of the water level corresponds to the voltage, and the volume of the container corresponds to the charge. The analogy can be written as:

Capacity to hold water Water volume / Water height

In the electrical case, capacitance is given by the formula:

C Q / V

Where C is the capacitance, Q is the charge, and V is the voltage.

Applying the Concept to Capacitance

Given a 9.00 V battery connected to a capacitor that stores a charge of 27.0 μC, we can calculate the capacitance using the formula:

C Q / V

Substituting the given values:

C 27.0 μC / 9.00 V

C 3.00 μF

So, the capacitance of the capacitor is 3.00 μF.

Effect of Voltage on Capacitance

Now, let's determine the charge stored when the same capacitor is connected to a 12.0 V battery. The capacitance remains the same (3.00 μF) because it is a property of the capacitor itself and does not change with the applied voltage.

Using the same formula C Q / V and rearranging it to solve for charge Q, we get:

Q C * V

Substituting the given values:

Q 3.00 μF * 12.0 V

Q 36.0 μC

So, the charge stored when the capacitor is connected to a 12.0 V battery is 36.0 μC.

Conclusion

Understanding the concept of capacitance can be challenging, but using analogies like the measuring cup and containers can make it easier. The relationship between capacitance, charge, and voltage is expressed by the formula C Q / V, which is a fundamental concept in electrical engineering and physics.

For more in-depth information, you can refer to the definition of capacitance on Wikipedia.