`[ML^(2)T^(-3)A^(-1)]` is the dimensional formula for

Options

A. Capacitance
B. Resistance
C. Resistivity
D. Potential difference

Answer

To find the physical quantity that corresponds to the dimensional formula \([ML^{2}T^{-3}A^{-1}]\), we can analyze the components of the formula step by step.

### Step 1: Understand the Components of the Dimensional Formula
The dimensional formula \([ML^{2}T^{-3}A^{-1}]\) consists of:
- \(M\): Mass
- \(L^{2}\): Area (length squared)
- \(T^{-3}\): Inverse of time cubed
- \(A^{-1}\): Inverse of electric current (Ampere)

### Step 2: Relate the Formula to Known Physical Quantities
To identify the physical quantity, we can relate the components to known formulas in physics.

1. **Capacitance (C)**:
- The formula for capacitance is \(C = \frac{Q}{V}\), where \(Q\) is charge and \(V\) is voltage.
- The dimensional formula for charge \(Q\) is \(I \cdot T\) (where \(I\) is current).
- Voltage \(V\) can be expressed as \(V = \frac{W}{Q}\) (work done per unit charge), where work \(W\) has the dimensional formula \(ML^{2}T^{-2}\).

2. **Voltage (V)**:
- From the above, we can express voltage as:
\[ V = \frac{ML^{2}T^{-2}}{I \cdot T} = \frac{ML^{2}T^{-2}}{A} \text{ (since } I = A\text{)} \]
- Thus, the dimensional formula for voltage \(V\) is:
\[ [ML^{2}T^{-3}A^{-1}] \]

### Step 3: Conclusion
From the analysis, we find that the dimensional formula \([ML^{2}T^{-3}A^{-1}]\) corresponds to the physical quantity of **Voltage (Potential Difference)**.

### Final Answer
The dimensional formula \([ML^{2}T^{-3}A^{-1}]\) is for **Voltage (Potential Difference)**.

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