Which of the following quantities has the S.I. unit kg `m^(2)s^(-3)A^(-2)` ?

Options

A. resistance
B. inductance
C. capacitance
D. magnetic flux.

Answer

To determine which quantity has the S.I. unit of kg m² s⁻³ A⁻², we can analyze the options provided.

### Step-by-Step Solution:

1. **Understanding the Units**:
- The unit kg m² s⁻³ A⁻² can be broken down into its components:
- kg (kilogram) is the unit of mass.
- m² (square meter) is the unit of area.
- s⁻³ (per second cubed) indicates a rate of change over time.
- A⁻² (per ampere squared) relates to electric current.

2. **Identifying Relevant Quantities**:
- We need to find a physical quantity that can be expressed in these units. Common electrical quantities to consider include resistance, capacitance, and inductance.

3. **Resistance (R)**:
- The formula for electrical resistance is given by Ohm's Law:
\[ R = \frac{V}{I} \]
where \( V \) is voltage (in volts) and \( I \) is current (in amperes).
- Voltage (V) can also be expressed in terms of energy:
\[ V = \frac{W}{Q} \]
where \( W \) is work done (in joules) and \( Q \) is charge (in coulombs).
- Therefore, resistance can also be expressed as:
\[ R = \frac{W}{Q \cdot I} \]

4. **Converting Units**:
- The unit of work (energy) is joules (J), which can be expressed as:
\[ 1 \text{ J} = 1 \text{ kg} \cdot \text{m}^2 \cdot \text{s}^{-2} \]
- Charge (Q) in coulombs can be expressed in terms of current and time:
\[ Q = I \cdot t \]
- Substituting this back into the resistance formula gives:
\[ R = \frac{kg \cdot m^2 \cdot s^{-2}}{(I \cdot t) \cdot I} = \frac{kg \cdot m^2}{s^2 \cdot I^2} \]
- Rearranging gives:
\[ R = \frac{kg \cdot m^2}{s^3 \cdot A^2} \]

5. **Conclusion**:
- Thus, the S.I. unit of resistance (R) is indeed kg m² s⁻³ A⁻². Therefore, the correct answer to the question is that resistance has the S.I. unit of kg m² s⁻³ A⁻².

### Final Answer:
The quantity that has the S.I. unit kg m² s⁻³ A⁻² is **Resistance (R)**.