Dimensional formula of 'ohm' is same as

Options

A. `h/e`
B. `h^2/e`
C. `h/(e^2)`
D. `h^2/e^2`

Answer

To find the dimensional formula of 'ohm' (Ω), we start with the definition of resistance in terms of potential difference (voltage) and current:

1. **Understanding Resistance**:
The formula for resistance (R) is given by:
\[ R = \frac{V}{I} \]
where \( V \) is the potential difference and \( I \) is the current.

2. **Finding the Dimension of Current (I)**:
The dimension of electric current \( I \) is given as:
\[ [I] = I \]

3. **Finding the Dimension of Potential Difference (V)**:
To find the dimension of potential difference, we need to express it in terms of electric field (E) and distance (d):
\[ V = E \cdot d \]
- The electric field \( E \) is defined as force per unit charge:
\[ E = \frac{F}{Q} \]
- The dimension of force \( F \) is:
\[ [F] = M L T^{-2} \]
- The dimension of charge \( Q \) can be expressed in terms of current:
\[ [Q] = I \cdot T \]
Therefore, the dimension of electric field \( E \) becomes:
\[ [E] = \frac{M L T^{-2}}{I T} = M L T^{-3} I^{-1} \]

4. **Finding the Dimension of Potential Difference (V)**:
Now substituting the dimension of electric field into the equation for potential difference:
\[ [V] = [E] \cdot [d] = (M L T^{-3} I^{-1}) \cdot L = M L^2 T^{-3} I^{-1} \]

5. **Finding the Dimension of Resistance (R)**:
Now we substitute the dimensions of \( V \) and \( I \) into the resistance formula:
\[ [R] = \frac{[V]}{[I]} = \frac{M L^2 T^{-3} I^{-1}}{I} = M L^2 T^{-3} I^{-2} \]

6. **Conclusion**:
The dimensional formula of 'ohm' (Ω) is:
\[ [R] = M L^2 T^{-3} I^{-2} \]