Question

Electric current in a wire is 6A. How many electrons flow through a given point in a time os 3 second​

Answer 1

Given :

• Current flowing through wire (I) = 6 A
• Time interval (t) = 3 seconds

To Find :

• Number of electrons flowing through the wire.

Formula Used :

• I = Q/t
• Q = ±ne

Explanation :

We are given Current flowing through the wire which is 6 Ampere, time interval is given as 3 seconds. We have to find number of electrons flowing through wire. We have to solve this question in two steps.

1) We have to use formula (I = Q/t) for calculating the charge flowing in the circuit. Where,

• I is current
• Q is Charge
• t is time interval

2) In second step we have to use formula for Quantisation of Charges. (Q = ± ne) . Where,

• Q is Charge
• n is number of electrons
• e is charge on electron

✯ Charge of the electron is $\sf{1.6 \: \times \: 10^{-19} \: C}$

Solution :

Now, we will calculate charge in wire

$\implies \sf{I \: = \: \dfrac{Q}{t}} \\ \\ \implies \sf{Q \: = \: It} \\ \\ \implies \sf{Q \: = \: 6 \: \times \: 3} \\ \\ \implies \sf{Q \: = \: 18}$

$\therefore$ Charge in the wire is 18 C.

___________________________

Now, We will calculate number of electrons passing through wire.

$\implies \sf{Q \: = \: ne} \\ \\ \implies \sf{n \: = \: \dfrac{Q}{e}} \\ \\ \implies \sf{n \: = \: \dfrac{18}{1.6 \: \times \: 10^{-19}}} \\ \\ \implies \sf{n \: = \: \dfrac{18 \: \times \: 10^{19}}{1.6}} \\ \\ \implies \sf{n \: = \: 11.25 \: \times \: 10^{19}}$

$\therefore$ Number of electrons passing through wire is $\sf{ 11.25 \: \times \: 10^{19}}$

Answer 2

Given ,

Electric current (I) = 6 amp

Time (t) = 3 sec

We know that ,

The rate of unit charge is called electric current

$\sf \star \: \: Electric \: current \: (I) = \frac{q}{t}$

Thus ,

$\Rightarrow \sf 6 = \frac{q}{3} \\ \\ \Rightarrow \sf q = 18 \: \: c$

Now , the charge is an integral multiples of electrons

$\star \: \: \sf Charge \: (q) = ne$

Thus ,

$\Rightarrow \sf 18 = n \times 1.6 \times {(10)}^{ - 19} \\ \\ \Rightarrow \sf n = 11.25 \times {(10)}^{19}$

$\therefore \underline{ \bold{ \sf{The \: number \: of \: electrons \: is \: 11.25 × {(10)}^{19} }}}$