Find the current through conductor at equals to 2 second if charge flowing through it varies with time as q equals to t square + 5

To find the current through a conductor at a specific time when the charge flowing through it varies with time, we can use the relationship between current (I) and charge (q). The current is defined as the rate of flow of charge, which can be mathematically expressed as:

Understanding the Relationship

The formula for current is given by:

I = dq/dt

Here, dq represents the change in charge, and dt represents the change in time. In your case, the charge q is defined as:

q(t) = t² + 5

Finding the Derivative

To find the current, we need to differentiate the charge function with respect to time:

dq/dt = d(t² + 5)/dt

Calculating this derivative:

• The derivative of t² is 2t.
• The derivative of a constant (5) is 0.

Thus, we have:

dq/dt = 2t

Calculating Current at t = 2 seconds

Now that we have the expression for current, we can substitute t = 2 seconds into the equation:

I = 2t

Substituting the value:

I = 2(2) = 4 A

Final Result

Therefore, the current through the conductor at t = 2 seconds is 4 Amperes.

Summary

In summary, by differentiating the charge function with respect to time, we found the current flowing through the conductor at a specific time. This process illustrates how calculus can be applied to understand electrical concepts, making it a powerful tool in physics and engineering.