Question

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

Answer 1

Hint: 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.