The dimensions of voltage in terms of mass (M), length (L) and time (T) and ampere (A) are

Options

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

Explanation

To find the dimensions of voltage in terms of mass (M), length (L), time (T), and ampere (A), we can follow these steps:

### Step 1: Understand the definition of Voltage
Voltage (V) is defined as the work done (W) per unit charge (Q). Mathematically, this can be expressed as:
\[ V = \frac{W}{Q} \]

### Step 2: Find the dimensions of Work Done
Work done is defined as force multiplied by displacement. The dimensions of force (F) are given by:
\[ F = MLT^{-2} \]
Displacement has the dimensions of length (L). Therefore, the dimensions of work done (W) can be calculated as:
\[ W = F \cdot \text{displacement} = (MLT^{-2}) \cdot L = ML^2T^{-2} \]

### Step 3: Find the dimensions of Charge
Charge (Q) is defined in terms of current (I), which is measured in amperes (A). The relationship between charge and current is given by:
\[ Q = I \cdot T \]
Thus, the dimensions of charge can be expressed as:
\[ Q = A \cdot T \]

### Step 4: Substitute the dimensions into the voltage formula
Now that we have the dimensions of work done and charge, we can substitute these into the voltage formula:
\[ V = \frac{W}{Q} = \frac{ML^2T^{-2}}{AT} \]

### Step 5: Simplify the expression
Now we simplify the expression for voltage:
\[ V = \frac{ML^2T^{-2}}{AT} = ML^2T^{-2} \cdot A^{-1}T^{-1} = ML^2T^{-3}A^{-1} \]

### Conclusion
Thus, the dimensions of voltage in terms of mass (M), length (L), time (T), and ampere (A) are:
\[ \text{Dimensions of Voltage} = ML^2T^{-3}A^{-1} \]

### Final Answer
The dimensions of voltage are \( ML^2T^{-3}A^{-1} \).

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