If charge $q = t^2 + 2t$ (in coulombs), find: (a) Current $i$ at $t...

Question

If charge $q = t^2 + 2t$ (in coulombs), find: (a) Current $i$ at $t = 2$ s (b) Average current from $t = 0$ to $t = 2$ s

Accepted Answer

or

(a) Instantaneous current $i = dq/dt = 2t + 2$

At $t = 2$ s:

$$i = 2(2) + 2 = 6 \text{ A}$$

(b) $q$ at $t = 2$ s: $q_2 = 4 + 4 = 8$ C

$q$ at $t = 0$: $q_0 = 0$ C

$$I_{avg} = \frac{\Delta q}{\Delta t} = \frac{8 - 0}{2} = 4 \text{ A}$$