Dimensional formula of the physical quantity, resistance is

Options

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

Answer

To find the dimensional formula of resistance, we can use Ohm's law, which states that:

\[ V = I \cdot R \]

From this, we can express resistance \( R \) as:

\[ R = \frac{V}{I} \]

### Step 1: Determine the dimensions of Voltage (V)
Voltage can be defined in terms of electric field (E) and distance (d):

\[ V = E \cdot d \]

The electric field \( E \) can be expressed as:

\[ E = \frac{F}{Q} \]

Where:
- \( F \) is force (with dimensions \( [M L T^{-2}] \))
- \( Q \) is charge (with dimensions \( [A T] \))

Now substituting for \( E \):

\[ V = \frac{F}{Q} \cdot d = \frac{[M L T^{-2}]}{[A T]} \cdot [L] \]

This simplifies to:

\[ V = \frac{M L^2}{A T^2} \]

### Step 2: Determine the dimensions of Current (I)
Current \( I \) is defined as charge per unit time:

\[ I = \frac{Q}{T} \]

The dimension of charge \( Q \) is \( [A T] \), thus:

\[ I = \frac{[A T]}{[T]} = [A] \]

### Step 3: Substitute the dimensions into the resistance formula
Now substituting the dimensions of \( V \) and \( I \) into the resistance formula:

\[ R = \frac{V}{I} = \frac{[M L^2 T^{-2} A^{-1}]}{[A]} \]

This simplifies to:

\[ R = [M L^2 T^{-2} A^{-2}] \]

### Final Step: Write the dimensional formula for resistance
Thus, the dimensional formula for resistance \( R \) is:

\[ R = [M L^2 T^{-3} A^{-2}] \]

### Answer
The dimensional formula of resistance is:

\[ [M L^2 T^{-3} A^{-2}] \]

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