# The current through a wire depends on the time as, i=(10+4t) . Here, i is in ampere t in seconds. find the charge crossed through a section in time interval between t=0 to t=10 sec ?

$300$

#### Explanation:

The electric current $I = 10 + 4 t$ , the rate of flow of charge $I = \frac{\mathrm{dQ}}{\mathrm{dt}}$, is the function of time then the charge crossed in differential time $\mathrm{dt}$ is given as follows

$\mathrm{dQ} = I \setminus \mathrm{dt}$

Now, integrating above equation from $t = 0$ to $t = 10 \setminus \sec$, we get the total charge crossed in given time interval

$Q = \setminus {\int}_{0}^{Q} \setminus \mathrm{dQ} = \setminus {\int}_{0}^{10} I \mathrm{dt}$

$Q = \setminus {\int}_{0}^{10} \left(10 + 4 t\right) \setminus \mathrm{dt}$

$= {\left(10 t + 2 {t}^{2}\right)}_{0}^{10}$

$= 10 \setminus \cdot 10 + 2 \setminus \cdot {10}^{2}$

$= 300$