Inductors

• Changing magnetic flux through a loop of wire creates electricty.
• The moving magnet means there's a changing flux through the coil so a voltage is induced in the circuit on the right and a current flows.

  
  

  Bottom diagram shows another coil. Changing current makes changing magnetic field meaning magnetic flux hitting right coil is changing.

  
  

  Change in flux in in the second coil is proportional to the changing current in the first. The proportionality constant is M.

  
• • A changing current goes through one coil of wire.
  • Current-carrying wires induce magnetic fields depending on the direction of the current. Therefore, this changing current creates a changing magnetic field.
  • This changing magnetic field goes through the middle of the second coil.
  • Changing flux causes an opposing induced emf (voltage).
  • Therefore, the second coil will have a current going through it, even though the two circuits aren't touching
• Mutual inductance and farday's law


  Equation: V2 = − ΔΦ2/Δt = −MΔI1/Δt

  
  

  This symbol M is called the mutual inductance of the two coils. It is measured in Henries, H

  
  

  Mutual inductance is when a changing current in one coil produces a changing flux in another separate coil and induces a voltage in that other coil
• Transformers

  Need AC electricity to work, and rely on mutual inductance.

  AC electricity is when the current is constantly

  going back and forth in the wires. Put two coils

  near each other, the alternating current in one coil will produce a current in the other.
• Primary coil has Np turns and secondary has Ns turns.

  
  

  If Np/Ns is greater than 1, step down transformer, If its smaller, step up transformer.

  
  

  This ratio as well as ratio between voltages: Np/Ns = Vp/Vs

  So step up transformers have higher induced voltage in secondary coil, step down transformers have lower induced voltage in secondary.
• Electrical power of primary coil is equal to electrical power of secondary coil. (all energy isn't lost)

  
  

  So Pp = Ps then VpIp = VsIs. -> equation to compare currents in the two coils
• Transformers rely on mutual inductance when the changing current (in the primary coil) is AC
• Self inductance: RL circut -> resistor and inductor

  Current from battery flows through circuit. Current in wire produces magnetic field around the wire. So if current from battery is flowing, there's flux through the inductor. If current changes there's a changing flux through the inductor.

  
  

  Changing flux induces a voltage. So seperate induced voltage (emf) coming from inductor is made inside the circuit (drives a current in opposite direction to the changing current).

  
• Self inductance

  Inductance is measured in Henries, H

  Changing flux in the inductor is proportional to the changing current through it. ∆Φ = L × ΔI

  L is the inductance (in H) of the inductor/coil. combine with ε = − ΔΦ/Δt -> ε = – L ΔI/Δt
• Inductors are wound up coils that go in circuits. The equation ε =– L ΔI/Δt tells us that a changing current will induce an (opposing) voltage across the inductor. The bigger the inductance L (in H), the bigger the induced voltage
• Total energy supplied to the circuit is the total flux multiplied by the current in the circuit: E = ΦI ->

  Φ = LI, so E = LI$^2$

  Inductor is only able to store half of this energy (the rest is dissipated). So the energy stored in the inductor is: E = 1/2 LI$^2$
• RL circuits

  It’s called an RL

  circuit because it has a resistor (R) and an inductor (L).

  Kirchhoff's law: Vs= VR + VL, Vs is batter voltage, VR is voltage across resistor, VL is voltage across the inductor

  Inductors oppose change. When current changes rapidly they are successful, overtime as current changes less rapidly they get weaker and eventually why current isn't changing they are hardly there.
• When the circuit is turned on current in circuit is zero. Inductors oppose increasing current so it builds slowly. Because I = 0, resistor voltage is 0 (Vr = IR) and Vs = VL

  VL shrinks overtime allowing VR to grow. Eventually VR = V. As VL shrinks and VR grows current grows too. Eventually circuit gets to a point where inductor hardly has an impact.

  
• When switch is closed in RL circuit, voltage across inductor starts at maximum and drops to zero exponentially. Resistor voltage starts at zero and rises to the maximum value (= to Vs) exponentially.

  τ represents the time taken for a 63% change and about 5 time constants means the process is complete. Equation: τ =L/R