Capacitors And Displacement Current

The displacement current is related to the rate of change of the charge on the capacitor, which is also related to the rate of change of the potential difference across the plates. The displacement current is given by: where: - is the capacitance of the capacitor, - is the rate of change of the potential difference. Given: - ,
- . We can solve for : Solving for :

Step 1: Understanding the Concept:
For a medium of given resistivity ( ) and permittivity ( ), the product of its resistance ( ) and capacitance ( ) is a constant that depends only on the material properties, not the geometry. This is derived from the relations and .
Step 2: Key Formula or Approach:
The fundamental relationship is:
Step 3: Detailed Explanation:
Given values: , F, , F/m. Substituting these into the formula: Comparing with , we get .
Step 4: Final Answer:
The value of is 2.

Step 1: Understanding the Question:
Displacement current is numerically equal to the conduction current flowing into the capacitor plates. We need to find the rate of change of voltage ( ) given and capacitance .
Step 2: Key Formula or Approach:

Step 3: Detailed Explanation:
Given and .
The relation is:



Rounding to two decimal places, we get .
Step 4: Final Answer:
The value of is 0.67.

Concept: When a dielectric slab fills part of the separation between plates (layered along thickness), the system behaves like capacitors in series. Original capacitance: Here the dielectric fills half the thickness .
Step 1:Capacitance of the air region}
Step 2:Capacitance of the dielectric region}
Step 3:Equivalent capacitance} Since they are in series:
Step 4:Substitute }
Step 5:Percentage increase}

Step 1: Identify the initial condition.
When the key is closed, the inductor will act as a short circuit initially (since the inductor's reactance is zero at the moment the circuit is first closed). Thus, the current will initially only be determined by the resistors. Step 2: Analyze the circuit.
The circuit consists of three resistors of 9 each in parallel, and the total resistance is given by: Step 3: Apply Ohm's law.
Using Ohm's law, the current is: However, as the inductors begin to oppose the change in current, the current will initially be lower. Therefore, just after the key is closed, the current is 1 A. Final Answer: