Question

The current in a conductor is expressed as I = 3t2 + 4t3 , where I is in Ampere and t is in second. The amount of electric charge that flows through a section of the conductor during t = 1s to t = 2s is ____________ C.

Answer 1

The electric charge $q$ is given by:

$q = \int_{t_1}^{t_2} I(t) \, dt$

Substituting $I(t) = 3t^2 + 4t$ and integrating from $t = 1 \, \text{s}$ to $t = 2 \, \text{s}$:

$q = \int_{1}^{2} (3t^2 + 4t) \, dt$

Calculating the integral:

$q = \left[ t^3 + 2t^2 \right]_{1}^{2} = \left( 2^3 + 2 \times 2^2 \right) - \left( 1^3 + 2 \times 1^2 \right)$

$q = (8 + 8) - (1 + 2) = 16 - 3 = 22 \, \text{C}$