Question

In a closed circuit, the electric current at any instant of time $t$ (in $sec$) is given by an equation $I=(4–0.08t)$$t=50s$. How many electrons flow through the circuit in $50s$?

Answer 1

Step 1: Given data

1. Current flowing in the circuit, $I=\left(4-0.08t\right)$
2. Required time, $t=50s$
3. Charge of electron, $e=1.6\times {10}^{-19}$C.

Step 2: Electric current

1. Electric current is the time rate of change in electric charge.
2. Electric current is defined by the form, $I=\frac{dq}{dt}$, where $q$ is the electric charge and $I$ is the current.

Step 3: Finding the total charge

We know that, $I=\frac{dq}{dt}$.

Now, $dq=Idt$

⇒$\int dq=\int Idt=\int \left(4-0.08t\right)dt$.

⇒$q={\int }_0^{50}\left(4-0.08t\right)dt$.

⇒$q={\left(4t-0.08\frac{t^2}{2}\right)}_0^{50}.$

⇒$q=100$.

Step 4: Finding the numbers of electron

Again we know, charge, $q=Ne$, where $N$ is the number of electrons and $e$ is the charge of electrons.

Therefore, the number of electrons,

$$\begin{gathered} N=\frac{q}{e}\frac{100}{1.6\times {10}^{-19}}=6.2\times {10}^{20}. \\ orN=6.2\times {10}^{20}. \end{gathered}$$

So, the number of electrons passing through the circuit in $50s$ is $6.2\times {10}^{20}$.