Question

When one computes the square root of the ratio of the permeability of free space to the permittivity of free space, one obtains $\sqrt{\frac{{\mu }_0}{{ϵ}_0}}=377$ What is the unit of this quantity?

• A. farads
• B. joules
• C. volts
• D. ohms

Answer 1

Answer: (D)

Unit of ${\mu }_0=$ ohm sec/meter
$C^2=\frac{1}{{\mu }_0{\in }_0}$
$C=$ velocity of light
$x\sqrt{\frac{{\mu }_0}{{ϵ}_0}}=\sqrt{{\mu }_0^2{C}^2}={\mu }_{0}C$
Unit of $C=$ metre/sec.
Unit of $\sqrt{\frac{{\mu }_0}{{ϵ}_0}}=$ unit of ${\mu }_{0}C=$ ohm sec/meter $\times$ meter/sec $=$ Ohm.