Dimension of electrical resistance is :-

Options

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

Explanation

To find the dimension of electrical resistance, we can start from Ohm's Law, which states that:

\[ V = IR \]

Where:
- \( V \) is the voltage (potential difference),
- \( I \) is the current,
- \( R \) is the resistance.

From this equation, we can express resistance \( R \) as:

\[ R = \frac{V}{I} \]

### Step 1: Determine the dimensions of voltage \( V \)

Voltage \( V \) can be expressed in terms of work done \( W \) and charge \( Q \):

\[ V = \frac{W}{Q} \]

The dimension of work \( W \) is given by:

\[ W = \text{Force} \times \text{Distance} = (M L T^{-2}) \times L = M L^2 T^{-2} \]

The dimension of charge \( Q \) is represented as:

\[ Q = I \times T \]

Where \( I \) is the current. Therefore, the dimension of charge \( Q \) is:

\[ Q = A T \]

Now substituting these into the equation for voltage:

\[ V = \frac{M L^2 T^{-2}}{A T} \]

This simplifies to:

\[ V = M L^2 T^{-3} A^{-1} \]

### Step 2: Determine the dimensions of current \( I \)

The dimension of current \( I \) is simply:

\[ I = A \]

### Step 3: Substitute dimensions of \( V \) and \( I \) into the equation for \( R \)

Now substituting the dimensions of \( V \) and \( I \) into the equation for resistance:

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

This simplifies to:

\[ R = M L^2 T^{-3} A^{-2} \]

### Conclusion

Thus, the dimension of electrical resistance \( R \) is:

\[ [R] = M L^2 T^{-3} A^{-2} \]