Question

Charge 'Q' (in coulomb) flowing through a conductor in terms of time 't' (in seconds) is given by the equation \( Q = 3t^2 + t \). The current in the conductor at time \( t = 3 \, \text{s} \) is:

• A. 3 A
• B. 7 A
• C. 19 A
• D. 21 A

Hint:

Remember that current is the rate of flow of charge: \( I = \frac{dQ}{dt} \). When given \( Q \) as a function of time, differentiate to find current.

Answer 1

The Correct Option is C

Step 1: Recall the relationship between charge and current.
Current \( I \) is the time derivative of charge \( Q \):
\[ I = \frac{dQ}{dt} \] Step 2: Differentiate the given equation.
Given: \( Q = 3t^2 + t \)
Differentiate with respect to \( t \):
\[ I = \frac{d}{dt}(3t^2 + t) = 6t + 1 \] Step 3: Substitute \( t = 3 \) s.
\[ I = 6(3) + 1 = 18 + 1 = 19 \, \text{A} \] Step 4: Select the correct option.
The calculated current is 19 A, which matches option (3).