$A$ current through a wire depends on time as $i = \alpha_{0} t + \beta t^{2}$ where $\alpha_{0} = 20 \, A/s$ and $\beta = 8 \, As^{-2}$. Find the charge crossed through a section of the wire in $15 \, s$ (in $C$).

The quantity $X = \frac{\varepsilon_0 LV}{t}$,where $\varepsilon_0$ is the permittivity of free space,$L$ is length,$V$ is potential difference,and $t$ is time. The dimensions of $X$ are the same as those of:

An electron (charge $= 1.6 \times 10^{-19} \text{ C}$) is moving in a circle of radius $5.1 \times 10^{-11} \text{ m}$ at a frequency of $6.8 \times 10^{15} \text{ rev/s}$. The equivalent current is approximately:

Define the $SI$ unit of electric charge in terms of the Ampere.

Current passing through a wire as a function of time is given as $I(t) = 0.02t + 0.01 \ A$. The charge that will flow through the wire from $t = 1 \ s$ to $t = 2 \ s$ is: (in $C$)

$A$ source of $e.m.f.$ $E = 15\,V$ and having negligible internal resistance is connected to a variable resistance so that the current in the circuit increases with time as $i = 1.2t + 3$. Then,the total charge that will flow in the first five seconds will be ............... $C$.