The dimensions of specific resistance are

Options

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

Explanation

To find the dimensions of specific resistance (also known as resistivity), we start with the formula for resistance \( R \):

\[ R = \frac{\rho L}{A} \]

Where:
- \( R \) is the resistance,
- \( \rho \) is the resistivity (specific resistance),
- \( L \) is the length of the conductor,
- \( A \) is the cross-sectional area of the conductor.

From this equation, we can express resistivity \( \rho \) as:

\[ \rho = \frac{R \cdot A}{L} \]

### Step 1: Determine the dimensions of resistance \( R \)

To find the dimensions of resistance, we can use the formula for heat generated in a resistor:

\[ H = I^2 R T \]

Where:
- \( H \) is the heat generated,
- \( I \) is the current,
- \( T \) is the time.

Rearranging gives us:

\[ R = \frac{H}{I^2 T} \]

### Step 2: Find the dimensions of heat \( H \)

The dimension of heat can be expressed as:

\[ [H] = ML^2T^{-2} \]

### Step 3: Find the dimensions of current \( I \)

The dimension of current \( I \) (in terms of ampere) is:

\[ [I] = A \]

### Step 4: Find the dimensions of time \( T \)

The dimension of time is:

\[ [T] = T \]

### Step 5: Substitute the dimensions into the resistance formula

Now substituting these dimensions into the resistance formula:

\[ [R] = \frac{ML^2T^{-2}}{(A^2)(T)} = \frac{ML^2T^{-2}}{A^2 T} = \frac{ML^2}{A^2 T^3} \]

Thus, the dimension of resistance \( R \) is:

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

### Step 6: Substitute into the resistivity formula

Now substituting the dimensions of \( R \) back into the resistivity formula:

\[ \rho = \frac{R \cdot A}{L} \]

Substituting the dimensions we have:

\[ [\rho] = \frac{ML^2T^{-3}A^{-2} \cdot L^2}{L} = ML^3T^{-3}A^{-2} \]

### Final Result

Thus, the dimensions of specific resistance (resistivity) are:

\[ [\rho] = ML^3T^{-3}A^{-2} \]