Question

Another unit for the quantity having the unit $\frac{C^2}{N{m}^2}$ is:

• A. $farad$
• B. $\frac{farad}{m^2}$
• C. $\frac{farad}{m}$
• D. $\frac{m}{farad}$

Answer 1

Answer: (C)

$\frac{farad}{m}$

Basically, $C$ is the unit of charge, whereas $Nm\left(orJ\right)$ is the unit of work done.
Therefore, $\frac{C}{Nm/C}$ $=$ $\frac{Q}{V}=$ Units of capacitance $=$ farad
Therefore, replacing this relation in the above expression,
$\frac{C^2}{N{m}^2}=\frac{farad}{m}$