The dimensional formula of electric potential is

Options

A. `[ML^(2)T^(-3)A^(1)]`
B. `[M^(-1)L^(2)T^(-2)A]`
C. `[M^(-1)L^(2)T^(-2)A^(-1)]`
D. `[ML^(2)T^(-2)A]`

Explanation

To find the dimensional formula of electric potential, we can follow these steps:

### Step 1: Understand the Definition of Electric Potential
Electric potential (V) is defined as the work done (W) per unit charge (Q). Mathematically, this can be expressed as:
\[ V = \frac{W}{Q} \]

### Step 2: Determine the Dimensional Formula of Work
Work is defined as the force applied over a distance. The formula for work is:
\[ W = F \cdot d \]
where:
- \( F \) is the force
- \( d \) is the distance

The dimensional formula for force (F) is given by:
\[ F = m \cdot a \]
where:
- \( m \) is mass (M)
- \( a \) is acceleration (L T⁻²)

Thus, the dimensional formula for force is:
\[ [F] = M L T^{-2} \]

Now, substituting this into the formula for work:
\[ [W] = [F] \cdot [d] = (M L T^{-2}) \cdot (L) = M L^2 T^{-2} \]

### Step 3: Determine the Dimensional Formula of Charge
The dimensional formula for electric charge (Q) is:
\[ [Q] = A T \]
where:
- \( A \) is the unit of electric current
- \( T \) is time

### Step 4: Combine the Dimensional Formulas
Now we can substitute the dimensional formulas of work and charge into the equation for electric potential:
\[ [V] = \frac{[W]}{[Q]} = \frac{M L^2 T^{-2}}{A T} \]

### Step 5: Simplify the Expression
Now, simplifying the expression:
\[ [V] = M L^2 T^{-2} \cdot (A T)^{-1} = M L^2 T^{-3} A^{-1} \]

### Final Result
Thus, the dimensional formula of electric potential is:
\[ [V] = M L^2 T^{-3} A^{-1} \]

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