Unit of `(CV)/(rho epsilon_(0))` are of
(`C =` capacitance, `V =` potential, `rho =` specfic resistence and `epsilon_(0) =` permittivity of free space)`

Options

A. charge
B. current
C. time
D. frequency

Answer

To find the unit of \((CV)/(\rho \epsilon_0)\), we will analyze the units of each component in the expression step by step.

### Step 1: Identify the units of each variable
1. **Capacitance (C)**: The unit of capacitance is Farad (F).
- \(1 \text{ F} = 1 \frac{\text{C}}{\text{V}}\) (Coulombs per Volt)

2. **Potential (V)**: The unit of electric potential is Volt (V).
- \(1 \text{ V} = 1 \frac{\text{J}}{\text{C}} = 1 \frac{\text{kg} \cdot \text{m}^2}{\text{s}^3 \cdot \text{C}}\)

3. **Specific Resistance (\(\rho\))**: The unit of specific resistance is Ohm-meter (\(\Omega \cdot m\)).
- \(1 \Omega = 1 \frac{\text{V}}{\text{A}} = 1 \frac{\text{kg} \cdot \text{m}^2}{\text{s}^3 \cdot \text{A}}\)

4. **Permittivity of Free Space (\(\epsilon_0\))**: The unit of permittivity is Farad per meter (F/m).
- \(1 \text{ F/m} = 1 \frac{\text{C}^2}{\text{N} \cdot \text{m}^2} = 1 \frac{\text{C}^2}{\text{kg} \cdot \text{m} \cdot \text{s}^2}\)

### Step 2: Substitute the units into the expression
Now we can substitute the units into the expression \((CV)/(\rho \epsilon_0)\).

\[ \text{Units of } CV = \text{Units of } C \times \text{Units of } V = \text{F} \times \text{V} \]

Substituting the units of Farad:
\[ \text{F} = \frac{\text{C}}{\text{V}} \Rightarrow CV = \text{C} \]

Thus,
\[ CV = \text{C} \cdot \text{V} = \text{C} \cdot \text{V} = \text{C} \cdot \frac{\text{J}}{\text{C}} = \text{J} \]

### Step 3: Calculate the denominator \(\rho \epsilon_0\)
Now, we will calculate the units of \(\rho \epsilon_0\):
\[ \text{Units of } \rho \epsilon_0 = \text{Units of } \rho \times \text{Units of } \epsilon_0 = \Omega \cdot m \times \frac{\text{F}}{m} \]

Substituting the units:
\[ \Omega = \frac{\text{V}}{\text{A}} \Rightarrow \rho \epsilon_0 = \left(\frac{\text{V}}{\text{A}}\right) \cdot \text{F/m} = \frac{\text{V}}{\text{A}} \cdot \frac{\text{C}^2}{\text{N} \cdot \text{m}^2} \]

### Step 4: Combine the units
Now, we can combine the units:
\[ \text{Units of } CV = \text{J} \quad \text{and} \quad \text{Units of } \rho \epsilon_0 = \Omega \cdot m \cdot \frac{\text{F}}{m} = \Omega \cdot \text{F} \]

Thus, the final units of \((CV)/(\rho \epsilon_0)\) are:
\[ \frac{\text{C} \cdot \text{V}}{\rho \epsilon_0} = \frac{\text{C} \cdot \text{V}}{\Omega \cdot \text{F}} = \text{A} \]

### Conclusion
The unit of \((CV)/(\rho \epsilon_0)\) is **Ampere (A)**, which corresponds to option B.