SI Unit Definitions for Physical Quantities

The question asks us to identify which physical quantity among the given options has an SI unit equivalent to one Weber per Ampere ($1 \text{ Wb/A}$) or one Volt-second per Ampere ($1 \text{ V}\cdot\text{s/A}$). We need to analyze the definition and standard SI units for each option provided.

Capacitance Unit Check ($C/V$)

Capacitance is a measure of a system's ability to store electric charge. It is defined as the ratio of the change in electric charge ($Q$) stored on a conductor to the corresponding change in its electric potential ($V$).

• Formula: $C = \frac{Q}{V}$
• SI Unit: The standard SI unit for capacitance is the Farad (F). From the formula, $1 \text{ Farad} = 1 \text{ Coulomb per Volt}$ ($1 \text{ C/V}$).

The unit of capacitance ($C/V$) does not match the units specified in the question ($Wb/A$ or $V \cdot s/A$).

Inductance Unit Derivation ($Wb/A$ and $V \cdot s/A$)

Inductance is a property of an electrical circuit element that opposes changes in the electric current flowing through it. This opposition arises due to the magnetic field generated by the current.

There are two common ways to define inductance and derive its units, both aligning with the question:

• Using Magnetic Flux: The magnetic flux ($\Phi_B$) linkage through a circuit is directly proportional to the current ($I$) flowing through it. The constant of proportionality is the inductance ($L$).
  • Relationship: $\Phi_B = L \cdot I$
  • Deriving the unit: Rearranging the formula gives $L = \frac{\Phi_B}{I}$.
  • Unit Calculation: The SI unit of magnetic flux is the Weber (Wb), and the SI unit of current is the Ampere (A). Therefore, the unit of inductance is $\frac{\text{Weber}}{\text{Ampere}}$, or $1 \text{ Wb/A}$.
• Using Induced Electromotive Force (EMF): Faraday's law of induction states that a changing magnetic flux induces an EMF ($\mathcal{E}$) in a circuit. For self-inductance, the induced EMF is proportional to the rate of change of current ($\frac{dI}{dt}$).
  • Relationship: $\mathcal{E} = -L \frac{dI}{dt}$
  • Deriving the unit: Rearranging for inductance gives $L = -\frac{\mathcal{E}}{dI/dt}$.
  • Unit Calculation: The SI unit of EMF is the Volt (V), and the SI unit for the rate of change of current is Amperes per second ($A/s$). Thus, the unit of inductance is $\frac{\text{Volt}}{\text{Ampere/second}}$, which simplifies to $\frac{V \cdot s}{A}$.

Both derived units, $1 \text{ Wb/A}$ and $1 \text{ V}\cdot\text{s/A}$, are equivalent and define the SI unit of inductance, which is named the Henry (H). This matches the description given in the question precisely.

Magnetic Field Strength Unit Check ($A/m$ and $T$)

Magnetic Field Strength can refer to two related quantities:

• Magnetic Field Intensity (H): This quantity measures the intensity of an externally applied magnetic field. Its SI unit is Amperes per meter ($A/m$).
• Magnetic Flux Density (B): This quantity represents the total magnetic flux passing through a unit area. Its SI unit is the Tesla (T). One Tesla is equivalent to one Weber per square meter ($1 \text{ T} = 1 \text{ Wb/m}^2$).

Neither the unit for Magnetic Field Intensity ($A/m$) nor Magnetic Flux Density ($T$ or $Wb/m^2$) matches the units $Wb/A$ or $V \cdot s/A$.

Magnetic Permeability Unit Check ($T \cdot m/A$)

Magnetic Permeability ($\mu$) quantifies a material's ability to support the formation of a magnetic field within itself. It describes how easily magnetic flux can pass through a substance.

• Relationship: It relates Magnetic Flux Density ($B$) and Magnetic Field Intensity ($H$) through the equation $B = \mu H$.
• Deriving the unit: Rearranging gives $\mu = \frac{B}{H}$.
• Unit Calculation: The SI unit of $B$ is Tesla (T), and the SI unit of $H$ is Ampere per meter ($A/m$). Therefore, the SI unit of permeability is Tesla-meter per Ampere ($T \cdot m/A$).
• Alternative Expression: Permeability is often expressed in units of Henry per meter ($H/m$), where H is the Henry. Since $1 \text{ H} = 1 \text{ V}\cdot\text{s/A}$, the unit becomes $\frac{V \cdot s}{A \cdot m}$.

The unit of magnetic permeability ($T \cdot m/A$ or $H/m$) does not match the units specified in the question.

Summary of Units

To summarize the analysis, let's compare the units of the given physical quantities:

Conclusion on Physical Quantity Units

Based on the detailed analysis of each option, Inductance is the physical quantity whose SI unit is defined as $1 \text{ Wb/A}$ or equivalently $1 \text{ V}\cdot\text{s/A}$. These units represent the Henry (H).