13.2 Inductance

• What is the unit of inductance?

  Henry
• Magnetic flux is symbolized by \Phi_{B}
• What is the magnetic flux if a magnetic field of 2 Tesla passes perpendicularly through an area of 3 square meters?

  6 Webers
• What is the unit of magnetic field strength?

  Tesla
• What is the relationship between magnetic flux, current, and inductance?

  L = \frac{N\Phi}{I}</latex>
• What does the symbol $L$ represent in the self-inductance formula?


  Self-inductance
• Inductance measures the ability of a conductor to oppose changes in current flow.


  True
• Steps in deriving the self-inductance formula using Faraday's law:

  1️⃣ The magnetic flux through a coil is related to inductance and current

  2️⃣ Faraday's law states the induced EMF is the rate of change of magnetic flux

  3️⃣ Substitute the expression for magnetic flux into Faraday's law

  4️⃣ Assume inductance is constant and take it out of the derivative

  5️⃣ Express inductance in terms of EMF and rate of change of current
• What law is used to describe the induced EMF in a coil when the current changes?

  Faraday's law
• Match the symbol with its description in mutual inductance:

  M ↔️ Mutual Inductance

  N2 ↔️ Number of turns in coil 2

  \Phi12 ↔️ Magnetic flux through coil 2 due to current in coil 1

  I1 ↔️ Current in coil 1
• Inductance is symbolized by L
• What is magnetic flux measured in?

  Webers
• Match the component with its unit:

  Magnetic Flux ↔️ Webers

  Magnetic Field Strength ↔️ Teslas

  Area Vector ↔️ Square Meters
• Inductance opposes changes in current
• Self-inductance describes the ability of a conductor to induce a voltage in itself when the current changes.


  True
• The magnetic flux through a coil with N turns is related to the current (I) by the definition of inductance
• What is the unit of mutual inductance?

  Henries (H)
• Magnetic flux is the total number of magnetic field lines passing through a given area
• Self-inductance is measured in henries
• Steps in deriving the self-inductance equation

  1️⃣ Start with the definition of inductance: $L =$$\frac{N\Phi}{I}$

  2️⃣ Rearrange the equation to $N\Phi =$$LI$

  3️⃣ Apply Faraday's law: $EMF =$$- \frac{d(N\Phi)}{dt}$

  4️⃣ Substitute $N\Phi$ into Faraday's law

  5️⃣ Assume L is constant: $EMF =$$- L\frac{dI}{dt}$

  6️⃣ Express L in terms of EMF and $\frac{dI}{dt}$
• Self-inductance opposes changes in current flow by inducing an EMF
• RL Circuits contain both resistors and inductors
• Energy stored in an inductor is released when the current decreases


  True
• The higher the magnetic flux for a given current, the higher the inductance.


  True
• Magnetic flux is the total magnetic field lines passing through a given area.

  True
• What is the inductance of a coil with 100 turns and a magnetic flux of 0.05 webers when a current of 5 amperes flows through it?

  1 Henry
• What is the magnetic flux if a magnetic field of 2 Tesla passes through an area of 3 square meters at an angle of 90 degrees?

  6 Webers
• What is the formula relating magnetic flux, number of turns, current, and inductance?

  $L =$$\frac{N\Phi}{I}$
• Match the symbol with its description in the self-inductance formula:

  $N$ ↔️ Number of turns in the coil

  $\Phi$ ↔️ Magnetic flux through each turn

  $I$ ↔️ Current flowing through the coil
• What is magnetic flux measured in?

  Webers (Wb)
• What is the final equation for self-inductance derived using Faraday's law?

  $L =$$- \frac{EMF}{\frac{dI}{dt}}$
• Self-inductance is constant over time if the current is changing


  True
• What is the primary difference between self-inductance and mutual inductance?

  One conductor vs. two coils
• What formula expresses mutual inductance between two coils?

  M = \frac{N_{2}\Phi_{12}}{I_{1}}</latex>
• What does the time constant in an RL circuit measure?

  Rate of current change
• Mutual inductance requires overlapping magnetic fields between two coils


  True
• In an RL circuit, current growth starts slowly due to the inductor's opposition

  True
• What formula expresses the energy stored in an inductor?

  $U =$$\frac{1}{2}LI^{2}$