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

Options

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

Explanation

To determine the physical quantity corresponding to the dimensions \([M^{1}L^{2}T^{-3}A^{-1}]\), we will analyze each option step by step.

### Step 1: Analyze the dimensions of Resistance
Resistance (\(R\)) is defined as voltage (\(V\)) divided by current (\(I\)):
\[ R = \frac{V}{I} \]
The dimensional formula for voltage (\(V\)) is given by:
\[ V = W/Q \]
Where \(W\) (work or energy) has dimensions \([M^{1}L^{2}T^{-2}]\) and \(Q\) (charge) has dimensions \([A^{1}T^{1}]\). Thus, the dimensional formula for voltage is:
\[ V = \frac{[M^{1}L^{2}T^{-2}]}{[A^{1}T^{1}]} = [M^{1}L^{2}T^{-3}A^{-1}] \]
The dimensional formula for current (\(I\)) is:
\[ I = [A^{1}] \]
Now substituting back into the resistance formula:
\[ R = \frac{[M^{1}L^{2}T^{-3}A^{-1}]}{[A^{1}]} = [M^{1}L^{2}T^{-3}A^{-2}] \]
This does not match our dimensions.

### Step 2: Analyze the dimensions of Resistivity
Resistivity (\(\rho\)) is defined as:
\[ \rho = R \cdot A/L \]
Where \(A\) is area and \(L\) is length. The dimensional formula for area (\(A\)) is \([L^{2}]\) and for length (\(L\)) is \([L^{1}]\). Thus, we can write:
\[ \rho = R \cdot \frac{[L^{2}]}{[L^{1}]} = R \cdot [L^{1}] \]
Using the dimensional formula for resistance from Step 1:
\[ \rho = [M^{1}L^{2}T^{-3}A^{-2}] \cdot [L^{1}] = [M^{1}L^{3}T^{-3}A^{-2}] \]
This does not match our dimensions.

### Step 3: Analyze the dimensions of Electrical Conductivity
Electrical conductivity (\(\sigma\)) is defined as:
\[ \sigma = \frac{1}{\rho} \]
Using the dimensional formula for resistivity from Step 2:
\[ \sigma = \frac{1}{[M^{1}L^{3}T^{-3}A^{-2}]} = [M^{-1}L^{-3}T^{3}A^{2}] \]
This does not match our dimensions.

### Step 4: Analyze the dimensions of Electromotive Force (EMF)
Electromotive force (EMF) is defined as:
\[ \text{EMF} = \frac{W}{Q} \]
Using the dimensions for work (\(W\)) and charge (\(Q\)) as defined earlier:
\[ \text{EMF} = \frac{[M^{1}L^{2}T^{-2}]}{[A^{1}T^{1}]} = [M^{1}L^{2}T^{-3}A^{-1}] \]
This matches our given dimensions.

### Conclusion
The physical quantity with dimensions \([M^{1}L^{2}T^{-3}A^{-1}]\) is **Electromotive Force (EMF)**.

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