Question

Determine the unit of'R'from dimensional analysis

Answer 1

Answer:

the dimensions are Mass L^2 Time^-2 Temp^-1 Mol^-1. where P is the pressure, V is the volume, n is the no of mole, R is gas constant and T is temperature.

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Answer 2

Answer:

Dimension for Resistance is  $[ML^2T^{-3}I^{-2}}]$

Explanation:

The dimension of a Physical quantity is defined as the way of expressing the physical quantity in terms of Fundamental quantities ( Mass, Length, Time, Current, Mole, Temperature, Luminous Intensity) and these quantities are specifically called 'derived quantities'.

By using ohm's law i.e. Voltage(V) = Current(I) X Resistance(R)

                                       Resistance(R) = Voltage(V) / Current(I) -----------(1)

The dimensional formula of voltage is:-

Voltage(V) = Electric field X Distance

                  = $\frac{Force}{Charge}\times Distance$

             $[V]= \frac{[M^1L^1T^{-2}]}{[IT^{-1}]}\times[L] =[ M^1 L^2T^{-3}I^{-1}]$

Substituting this dimension of voltage is equation(1), we get:-

            $[R]=\frac{[ M^1 L^2T^{-3}I^{-1}]}{[I]}=[ M^1 L^2T^{-3}I^{-2}]$

Therefore, the dimensional unit of resistance is $[ML^2T^{-3}I^{-2}}]$.