Question

The physical quantity which is measure in the unit of wb A^-1 is

• A. Self inductance
• B. Mutual inductance
• C. Magnetic flux
• D. Both (A) and (B)

Answer 1

The Correct Option is D

Step 1: Understand the given unit

The given unit is Weber per Ampere (Wb A^-1). We need to identify the physical quantity that has this unit.

Step 2: Recall the definition and formula for Self inductance (L)

Self inductance is the property of a coil by virtue of which it opposes any change in the current flowing through it. The induced emf (e) in a coil due to self inductance is given by:

$e = -L \frac{dI}{dt}$

where:

- e is the induced electromotive force (emf) in Volts (V)
- L is the self inductance
- $\frac{dI}{dt}$ is the rate of change of current in Ampere per second (A/s)

From the formula, we can express self inductance (L) as:

$L = -\frac{e}{\frac{dI}{dt}}$

Step 3: Determine the unit of Self inductance

Using the formula for L, we can derive the unit of self inductance:

Unit of L = Unit of (e) / Unit of ($\frac{dI}{dt}$)
Unit of L = Volt / (Ampere / second)
Unit of L = (Volt × second) / Ampere

We know that 1 Volt = 1 Weber / second (from Faraday's law of induction, $e = -\frac{d\Phi}{dt}$, where magnetic flux $\Phi$ is in Weber and time t is in seconds).
Substituting Volt = Weber / second into the unit of L:

Unit of L = ((Weber / second) × second) / Ampere
Unit of L = Weber / Ampere = Wb A^-1

Step 4: Recall the definition and formula for Mutual inductance (M)

Mutual inductance is the property of two coils by virtue of which each opposes any change in the current in the other. The induced emf ($e_2$) in a secondary coil due to the change in current in a primary coil ($I_1$) is given by:

$e_2 = -M \frac{dI_1}{dt}$

where:

- $e_2$ is the induced emf in the secondary coil in Volts (V)
- M is the mutual inductance
- $\frac{dI_1}{dt}$ is the rate of change of current in the primary coil in Ampere per second (A/s)

From the formula, we can express mutual inductance (M) as:

$M = -\frac{e_2}{\frac{dI_1}{dt}}$

Step 5: Determine the unit of Mutual inductance

Using the formula for M, we can derive the unit of mutual inductance:

Unit of M = Unit of ($e_2$) / Unit of ($\frac{dI_1}{dt}$)
Unit of M = Volt / (Ampere / second)
Unit of M = (Volt × second) / Ampere

Again, substituting Volt = Weber / second:

Unit of M = ((Weber / second) × second) / Ampere
Unit of M = Weber / Ampere = Wb A^-1

Step 6: Recall the unit of Magnetic flux

The unit of magnetic flux is Weber (Wb).

Step 7: Determine the correct option

From Step 3 and Step 5, we found that both Self inductance and Mutual inductance have the unit Wb A^-1.

Therefore, the physical quantity which is measured in the unit of Wb A^-1 is both Self inductance and Mutual inductance.

Final Answer: The final answer is ${Both (A) and (B)}$

Answer 2

We are looking for the physical quantity measured in the unit of Wb A^-1. Recall that 1 Weber (Wb) is the unit of magnetic flux.

Inductance

Self-inductance ($L$) and mutual inductance ($M$) are both defined by the relationship between induced voltage and the rate of change of current. Both have units of $\text{Wb} \cdot \text{A}^{-1}$ commonly known as the Henry (H):

For Self Inductance $\mathcal{E} = -L \frac{dI}{dt} $ and thus $ L= -\frac{\mathcal{E} dt}{dI} $ which has units of Volt-second/Ampere = (Joule/Coulomb) x Second/Ampere = Joule-second/(Ampere x Coulomb)= Weber/Ampere Similarily for mutual inductance, we have $\mathcal{E} = -M \frac{dI}{dt} $ and thus $ M= -\frac{\mathcal{E} dt}{dI} $

Magnetic Flux is measured in Webers (Wb). Thus Wb A^-1 is not the unit of magnetic flux.

Therefore, the physical quantities measured in Wb A^-1 are self-inductance and mutual inductance.

The correct answer is (D) Both (A) and (B).