In the given circuit,with steady current ,calculate the potential difference across the capacitor and the charge stored in it.Please give a detailed explanation to understand .

To calculate the potential difference across a capacitor and the charge stored in it when there is a steady current in the circuit, we need to understand a few fundamental concepts about capacitors and how they operate in a circuit. Let's break this down step by step.

Understanding Capacitors

A capacitor is a device that stores electrical energy in an electric field. It consists of two conductive plates separated by an insulating material called a dielectric. The key parameters we need to consider are:

• Capacitance (C): This is the ability of a capacitor to store charge per unit voltage, measured in farads (F).
• Charge (Q): The amount of electric charge stored in the capacitor, measured in coulombs (C).
• Voltage (V): The potential difference across the capacitor, measured in volts (V).

Basic Relationships

The relationship between charge, capacitance, and voltage is given by the formula:

Q = C × V

Where:

• Q is the charge stored in the capacitor.
• C is the capacitance of the capacitor.
• V is the potential difference across the capacitor.

Steady Current in the Circuit

When a steady current (I) flows through a circuit containing a capacitor, it means that the capacitor is charging or discharging at a constant rate. The current flowing into the capacitor can be related to the charge stored in it over time:

I = dQ/dt

Where:

• I is the current in amperes (A).
• dQ is the change in charge over time.
• dt is the change in time.

Calculating Charge and Voltage

To find the charge stored in the capacitor after a certain time (t), we can rearrange the current formula:

Q = I × t

Now, substituting this into the capacitance formula gives us:

V = Q / C = (I × t) / C

Example Calculation

Let’s say we have a capacitor with a capacitance of 10 microfarads (10 x 10^-6 F) and a steady current of 2 milliamperes (2 x 10^-3 A) flowing for 5 seconds. We can calculate the charge and the potential difference as follows:

Step 1: Calculate Charge (Q)

Using the formula:

Q = I × t

Substituting the values:

Q = (2 x 10^-3 A) × (5 s) = 10 x 10^-3 C = 0.01 C

Step 2: Calculate Voltage (V)

Now, using the capacitance formula:

V = Q / C

Substituting the values:

V = 0.01 C / (10 x 10^-6 F) = 1000 V

Summary of Results

In this example, after 5 seconds of steady current, the charge stored in the capacitor is 0.01 coulombs, and the potential difference across the capacitor is 1000 volts. This illustrates how the current, time, and capacitance work together to determine the charge and voltage in a capacitor.

Understanding these relationships is crucial for analyzing circuits that include capacitors, especially in applications like filtering, timing, and energy storage. If you have any further questions or need clarification on any part of this process, feel free to ask!