Plancks constant has the dimensions of:

CONCEPT:

• Measurement of any physical quantity involves comparison with a certain basic, arbitrarily chosen, internationally accepted reference standard called unit, and a Dimension is a mathematical tool used for studying the nature of physical quantities. 
• The basic concept of dimensions is that we can add or subtract only those quantities which have the same dimensions.
• And the dimensional formula is defined as the expression of the physical quantity in terms of mass, length, and time.

EXPLANATION:

Planck’s constant

• It is a physical constant that is the quantum of electromagnetic action. It relates the energy carried by a photon to its frequency by, E = hν.

\(⇒ h = \frac{E}{\nu }\)

Where, E = energy, ν = frequency and h = Planck’s constant.

Now,

• Dimensional formula of energy (E) = [ML2T-2]
• Dimensional formula of frequency (ν) = [T-1]
• The dimension of the plack constant is (h)

\(⇒ h = \frac{{M{L^2}{T^{ - 2}}}}{{{T^{ - 1}}}}=[ML^2T^{-1}]\)

Angular momentum:

• It is the rotational equivalent of linear momentum.         

⇒ L = r x p

Where, L = angular momentum, r = distance and p = linear momentum.

Now,

Dimensional formula of (r) = [L],

Dimensional formula of (p) = [MLT-1],

• Therefore, the dimensional formula of L is

⇒ L = [L] × [MLT-1]

⇒  L = [ML²T^-1]