Question

Prove that $1{\text{ }}coulomb = 3 \times {10^9}stat{\text{ }}coulomb$.

Answer 1

The electron charge, which is equal to $1.6 \times {10^{ - 19}}\;$ coulomb, is a fundamental physical constant that expresses the naturally occurring unit of electric charge.
One coulomb $\left( C \right)$ of charge is equal to $6.24 \times {10^{18}}\;$ electrons. The quantity of charge $\left( Q \right)$ on an object is equal to the number of elementary charges on the object $\left( N \right)$ multiplied by the elementary charge $\left( e \right)$

Complete step-by-step solution:
Coulomb is the derived SI unit of electric charge. It is the quantity of electricity transported in one second by a current of one ampere.
The stat coulomb is the physical unit for electrical charges used in the CGS units. It is a derived unit given by -
1 statcoulomb = 0.1 A m / c ; where c is the speed of light.
While absolute coulomb is defined as the amount of electric charge that crosses a surface in $1$ second, when a steady current of $1$ absolute ampere is flowing across the surface.
$1$ absolute coulomb = $10$ coulomb
$1$ absolute coulomb = $10$ coulomb = $\;3 \times {10^{10}}$ statC
Thus,
As the charge on an electron = $4.8 \times {10^{ - 10}}$ stat C
so, $1.6 \times {10^{ - 19}}$ C = $4.8 \times {10^{ - 10}}$ stat C
$1$ coulomb = $\dfrac{{4.8 \times {{10}^{ - 10}}}}{{1.6 \times {{10}^{ - 19}}}}$
$1$ coulomb =$\;3 \times {10^9}$ statC

Note:

It's important to remember that electrical conductivity and resistivity are inversely related, which means the more conductive something is, the less resistive it is.
By utilizing the resistance of a conductor, light is often created in an incandescent light bulb. In an incandescent light bulb, there's a wire filament that's a particular length and width, thus providing a particular resistance.