Choose the correct option:
If C represents capacitance and R represents resistance, then the unit of `CR^2` are

Options

A. (a) `Henry`
B. (b) `("volt-second")/("ampere")`
C. (c) `("volt")/("ampere")`
D. (d) `("joule")/("ampere"^(2))`

Answer

To find the unit of \( CR^2 \), where \( C \) represents capacitance and \( R \) represents resistance, we will follow these steps:

### Step 1: Identify the units of capacitance and resistance
- The unit of capacitance \( C \) is **Farad (F)**.
- The unit of resistance \( R \) is **Ohm (Ω)**.

### Step 2: Express the units in terms of base SI units
- The Farad is defined as \( 1 \, \text{F} = 1 \, \text{C/V} = 1 \, \text{C/(A·s)} \).
- The Ohm is defined as \( 1 \, \Omega = 1 \, \text{V/A} = 1 \, \text{(kg·m²)/(s³·A²)} \).

### Step 3: Calculate the unit of \( R^2 \)
- The unit of \( R^2 \) is:
\[ R^2 = (\Omega)^2 = \left(\frac{\text{V}}{\text{A}}\right)^2 = \frac{\text{V}^2}{\text{A}^2} \]

### Step 4: Combine the units of \( C \) and \( R^2 \)
- Now we can find the unit of \( CR^2 \):
\[ CR^2 = \text{F} \cdot R^2 = \text{F} \cdot \frac{\text{V}^2}{\text{A}^2} \]

### Step 5: Substitute the unit of capacitance
- Substituting the unit of capacitance:
\[ CR^2 = \left(\frac{\text{C}}{\text{V}}\right) \cdot \frac{\text{V}^2}{\text{A}^2} = \frac{\text{C} \cdot \text{V}}{\text{A}^2} \]

### Step 6: Convert units to find the final result
- Since \( \text{C} = \text{A} \cdot \text{s} \), we can rewrite the unit:
\[ CR^2 = \frac{\text{A} \cdot \text{s} \cdot \text{V}}{\text{A}^2} = \frac{\text{s} \cdot \text{V}}{\text{A}} = \text{V} \cdot \text{s} / \text{A} \]

### Conclusion
- The unit of \( CR^2 \) can also be expressed as **Volt-second per Ampere (V·s/A)**, which corresponds to option B.

### Final Answer
- The correct option is **B: Volt second per ampere**.

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