The electric current in a wire varies with ti | vedclass

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(A) The relationship between current $i$ and charge $q$ is given by $i = \frac{dq}{dt}$.Therefore,$dq = i \cdot dt = (2 + 3t) \cdot dt$.To find the to

Vedclass · Accepted Answer

$170$

Vedclass · Answer

(A) The relationship between current $i$ and charge $q$ is given by $i = \frac{dq}{dt}$.Therefore,$dq = i \cdot dt = (2 + 3t) \cdot dt$.To find the total charge $Q$ passed in $10 	ext{ s}$,we integrate from $t = 0$ to $t = 10 	ext{ s}$:$Q = \int_{0}^{10} (2 + 3t) \cdot dt$$Q = [2t + \frac{3t^2}{2}]_{0}^{10}$Substituting the limits:$Q = (2(10) + \frac{3(10)^2}{2}) - (0 + 0)$$Q = 20 + \frac{3 	imes 100}{2}$$Q = 20 + 150 = 170 	ext{ C}$.

The electric current in a wire varies with time as $i = (2 + 3t) \text{ A}$. Calculate the charge that passes through the cross-section of the wire in $10 \text{ s}$.

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