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.