Dielectrics in capacitors | Circuits | Physics | Khan Academy

Summary

This video explains how a dielectric material, a non-conducting substance placed between capacitor plates, increases capacitance. It prevents the metal plates from touching, ensuring charge storage, and causes the polarization of atoms in the dielectric material. This polarization reduces the voltage between the plates, increasing capacitance. The script explores two scenarios: one where the battery is disconnected, and the charge remains the same, and another where the battery is connected, increasing the stored charge. The dielectric constant is introduced as a way to quantify how much capacitance increases, with the formula C' = k × C, where k is always greater than 1.

Takeaways

• 😀 A non-conducting material, called a dielectric, is placed between capacitor plates to prevent the metal plates from touching each other.
• 😀 The primary purpose of the dielectric is to prevent direct contact between the plates, which would cause the capacitor to lose its charge storage capability.
• 😀 Inserting a dielectric always increases the capacitance of a capacitor, as long as the area and separation between the plates remain unchanged.
• 😀 The dielectric material polarizes when placed between the capacitor plates, meaning the negative side of atoms aligns with the positive plate, and the positive side aligns with the negative plate.
• 😀 The polarization of the dielectric reduces the voltage across the capacitor plates, even though the total charge remains the same.
• 😀 A lower voltage across the plates, with the same amount of charge, results in increased capacitance, according to the definition of capacitance.
• 😀 If the battery remains connected when the dielectric is inserted, the voltage across the capacitor stays constant, but the battery supplies more charge to maintain the voltage, further increasing capacitance.
• 😀 The increase in capacitance when the battery is connected occurs because the battery adds more charge to compensate for the voltage reduction caused by the dielectric.
• 😀 The dielectric constant (represented by k or kappa) is a key factor in determining how much the capacitance will increase when a dielectric is inserted.
• 😀 The capacitance after inserting a dielectric is calculated by multiplying the original capacitance by the dielectric constant (k), and since k is always greater than 1, capacitance will always increase.

Q & A

Why is a non-conducting material placed between the plates of a capacitor?

A non-conducting material is placed between the plates to prevent the metal plates from touching each other, which would short-circuit the capacitor and prevent charge from being stored.

What is the effect of inserting a non-conducting material (dielectric) between the plates of a capacitor?

Inserting a dielectric increases the capacitance of the capacitor by reducing the voltage between the plates, allowing more charge to be stored for the same voltage.

What is a dielectric?

A dielectric is a non-conducting material placed between the plates of a capacitor. It increases the capacitance by affecting the voltage and charge distribution within the capacitor.

How does a dielectric material reduce the voltage between the plates of a charged capacitor?

When a dielectric is placed between the plates, the molecules within the dielectric become polarized, with negative charges aligning near the positive plate and positive charges near the negative plate. This polarization cancels out some of the voltage between the plates.

What happens to the charge on the capacitor when a dielectric is inserted while the battery is disconnected?

When a dielectric is inserted with the battery disconnected, the charge on the capacitor remains the same, but the voltage decreases due to the polarization of the dielectric, which increases the capacitance.

What happens to the charge on the capacitor when a dielectric is inserted while the battery remains connected?

When a dielectric is inserted with the battery connected, the voltage across the capacitor stays the same as the battery’s voltage. However, the battery will supply additional charge to the capacitor to maintain this constant voltage, increasing the stored charge and thus increasing the capacitance.

What is the dielectric constant, and how does it affect capacitance?

The dielectric constant (represented by kappa or k) is a measure of how much a dielectric material increases the capacitance of a capacitor. The capacitance after inserting the dielectric is the product of the dielectric constant and the original capacitance.

How can you calculate the new capacitance after inserting a dielectric?

To calculate the new capacitance, multiply the original capacitance (C) by the dielectric constant (k). The formula is C' = k * C, where C' is the capacitance after inserting the dielectric.

What is the relationship between the dielectric constant and capacitance?

The dielectric constant is always greater than 1 for non-conducting materials, meaning that the insertion of a dielectric always increases the capacitance of a capacitor.

Can the type of dielectric material affect the capacitance increase?

Yes, the type of dielectric material affects the extent to which the capacitance increases, as each material has its own dielectric constant. A higher dielectric constant leads to a larger increase in capacitance.