Which of the following is not a dimensionless quantity?
Relative magnetic permeability $\left(\mu_{{r}}\right)$
Power factor
Permeability of free space $\left(\mu_{0}\right)$
Quality factor
$A$ and $B$ possess unequal dimensional formula then following operation is not possible in any case:-
Match the following two coloumns
Column $-I$ | Column $-II$ |
$(A)$ Electrical resistance | $(p)$ $M{L^3}{T^{ - 3}}{A^{ - 2}}$ |
$(B)$ Electrical potential | $(q)$ $M{L^2}{T^{ - 3}}{A^{ - 2}}$ |
$(C)$ Specific resistance | $(r)$ $M{L^2}{T^{ - 3}}{A^{ - 1}}$ |
$(D)$ Specific conductance | $(s)$ None of these |
In a particular system of units, a physical quantity can be expressed in terms of the electric charge $c$, electron mass $m_c$, Planck's constant $h$, and Coulomb's constant $k=\frac{1}{4 \pi \epsilon_0}$, where $\epsilon_0$ is the permittivity of vacuum. In terms of these physical constants, the dimension of the magnetic field is $[B]=[c]^\alpha\left[m_c\right]^\beta[h]^\gamma[k]^\delta$. The value of $\alpha+\beta+\gamma+\delta$ is. . . . .
If pressure $P$, velocity $V$ and time $T$ are taken as fundamental physical quantities, the dimensional formula of force is