The physical quantity having the dimensions `[M^(-1)L^(-3)T^(3)A^(2)]` is

Options

A. resistance
B. resistivity
C. electrical conductivity
D. electromotive force

Answer

To determine the physical quantity that has the dimensions \([M^{-1}L^{-3}T^{3}A^{2}]\), we will analyze the options provided: resistance, resistivity, electrical conductivity, and electromotive force.

### Step-by-Step Solution:

1. **Identify the Dimensions of Each Option**:
- **Resistance (R)**: The dimension of resistance is given by \(R = \frac{V}{I}\), where \(V\) (voltage) has dimensions of \([M L^{2} T^{-3} A^{-1}]\) and \(I\) (current) has dimensions of \([A]\). Thus, the dimensions of resistance are:
\[ [R] = \frac{[M L^{2} T^{-3} A^{-1}]}{[A]} = [M L^{2} T^{-3} A^{-2}] \]

- **Resistivity (\(\rho\))**: The dimension of resistivity is defined as resistance per unit length:
\[ [\rho] = [R] \cdot [L] = [M L^{2} T^{-3} A^{-2}] \cdot [L] = [M L^{3} T^{-3} A^{-2}] \]

- **Electrical Conductivity (\(\sigma\))**: Conductivity is the inverse of resistivity:
\[ [\sigma] = \frac{1}{[\rho]} = \frac{1}{[M L^{3} T^{-3} A^{-2}]} = [M^{-1} L^{-3} T^{3} A^{2}] \]

- **Electromotive Force (EMF)**: The dimension of EMF is equivalent to voltage, which is:
\[ [V] = [M L^{2} T^{-3} A^{-1}] \]

2. **Compare the Dimensions**:
- From the calculations:
- Resistance: \([M L^{2} T^{-3} A^{-2}]\)
- Resistivity: \([M L^{3} T^{-3} A^{-2}]\)
- Electrical Conductivity: \([M^{-1} L^{-3} T^{3} A^{2}]\)
- Electromotive Force: \([M L^{2} T^{-3} A^{-1}]\)

3. **Identify the Correct Option**:
- The dimensions \([M^{-1} L^{-3} T^{3} A^{2}]\) match with the dimensions of electrical conductivity.

### Conclusion:
The physical quantity having the dimensions \([M^{-1}L^{-3}T^{3}A^{2}]\) is **Electrical Conductivity**.