the dimensions of electric currect in electric conductivity are

Options

A. 1
B. 2
C. 3
D. `-2`

Answer

To find the dimensions of electric current in electric conductivity, we will follow these steps:

### Step 1: Understand the definition of electric conductivity
Electric conductivity (σ) is defined as the reciprocal of resistivity (ρ). Mathematically, this can be expressed as:
\[ \sigma = \frac{1}{\rho} \]

### Step 2: Identify the units of resistivity
The unit of resistivity (ρ) is ohm-meter (Ω·m).

### Step 3: Determine the unit of conductivity
Since conductivity is the reciprocal of resistivity, the unit of conductivity will be:
\[ \text{Unit of } \sigma = \frac{1}{\text{Unit of } \rho} = \frac{1}{\Omega \cdot m} \]
This can also be expressed in terms of siemens (S):
\[ \text{Unit of } \sigma = \text{S/m} \]

### Step 4: Convert the unit of conductivity to base units
The siemens (S) is defined as:
\[ 1 \, \text{S} = 1 \, \frac{\text{A}}{\text{V}} = 1 \, \frac{\text{A}}{\text{(kg} \cdot \text{m}^2/\text{s}^3)} = 1 \, \text{A} \cdot \text{s}^3/\text{kg} \cdot \text{m}^2 \]
Thus, the unit of conductivity can be expressed as:
\[ \text{S/m} = \frac{\text{A} \cdot \text{s}^3}{\text{kg} \cdot \text{m}^2 \cdot \text{m}} = \frac{\text{A} \cdot \text{s}^3}{\text{kg} \cdot \text{m}^3} \]

### Step 5: Write the dimensional formula for conductivity
From the unit of conductivity, we can derive the dimensional formula:
\[ [\sigma] = \frac{[A] \cdot [T]^3}{[M] \cdot [L]^3} \]
This can be expressed in terms of dimensions:
\[ [\sigma] = M^{-1} L^{-3} T^3 A^1 \]

### Step 6: Identify the power of electric current (A) in the dimensional formula
From the dimensional formula of conductivity, we can see that the power of electric current (A) is:
\[ A^1 \]

### Conclusion
Thus, the dimensions of electric current in electric conductivity are given by the power of A, which is 2.

### Final Answer
The power of A in the dimensional formula of electric conductivity is **2**.

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