calculate the dimensional formula of electric potential
Answers
Explanation:
Dimensional Formula of Electric Potential
M = Mass.
I = Current.
L = Length.
T = Time.
#BAL
The dimensional formula of electric potential is given by,
[M1 L2 T-3 I-1]
Where,
M = Mass
I = Current
L = Length
T = Time
Derivation
Since, Potential energy = Charge of particle × Electric potential
Therefore, electric potential = Potential energy × [Charge of a particle]-1 . . . . (1)
Since, electric charge = electric current × time
∴ The dimentional formula of electric charge = [I1 T1] . . . . . (2)
Since, Potential Energy = M × g × h . . . . . . (3)
The dimensions of height (h) and Mass (M) = [M0 L1 T0] and [M1 L0 T0] . . . . (4)
And, the dimensional formula of acceleation due to gravity (g) = [M0 L1 T-2] . . . . (5)
On substituting equation (4) and (5) in equation (3) we get,
Potential Energy = [M1 L0 T0] × [M0 L1 T-2] × [Mo L1 T0]
Therefore, the dimension of potential energy = [M1 L2 T-2] . . . . (6)
On substituting equation (2) and (6) in equation (1) we get,
Electric potential = Potential energy × [Charge of particle]-1
Or, Ep = [M1 L2 T-2] × [I1 T1]-1 = [M1 L2 T-3 I-1]
Therefore, the electric potential is dimensionally represented as [M1 L2 T-3 I-1].