If M = mass, L = length, T = time and I = electric current, then the demensional formula of resistance R will be given by

Options

A. `[R]=[ML^2T^-3I^-2]`
B. `[R]=[ML^2T^-3I^2]`
C. `[R]=[ML^2T^3I^-2]`
D. `[R]=[ML^2T^3I^2]`

Explanation

To find the dimensional formula of resistance \( R \), we can start from Ohm's law and work through the necessary steps.

### Step-by-Step Solution:

1. **Understand Ohm's Law**: According to Ohm's law, the relationship between potential difference \( V \), current \( I \), and resistance \( R \) is given by:
\[ V = I \cdot R \]
Therefore, we can express resistance as:
\[ R = \frac{V}{I} \]

2. **Express Potential Difference**: The potential difference \( V \) can also be expressed in terms of work done \( W \) and charge \( Q \):
\[ V = \frac{W}{Q} \]

3. **Dimensional Formula for Work**: The work done \( W \) has the dimensional formula:
\[ [W] = M L^2 T^{-2} \]

4. **Dimensional Formula for Charge**: The charge \( Q \) can be expressed in terms of current \( I \) and time \( T \):
\[ Q = I \cdot T \]
Thus, the dimensional formula for charge is:
\[ [Q] = I T \]

5. **Substituting into the Expression for \( V \)**: Now we can substitute the dimensional formulas for \( W \) and \( Q \) into the expression for \( V \):
\[ V = \frac{W}{Q} = \frac{M L^2 T^{-2}}{I T} = \frac{M L^2 T^{-2}}{I T} = M L^2 T^{-3} I^{-1} \]

6. **Substituting \( V \) back into the Expression for \( R \)**: Now we can substitute this expression for \( V \) back into the equation for resistance:
\[ R = \frac{V}{I} = \frac{M L^2 T^{-3} I^{-1}}{I} = M L^2 T^{-3} I^{-2} \]

7. **Final Dimensional Formula for Resistance**: Thus, the dimensional formula for resistance \( R \) is:
\[ [R] = M L^2 T^{-3} I^{-2} \]

### Conclusion:
The dimensional formula of resistance \( R \) is given by:
\[ [R] = M L^2 T^{-3} I^{-2} \]