Electromagnetic induction is the process by which kinetic energy is converted into electrical energy in the presence of a magnetic field.
How can we determine the magnitude and direction of induced EMF? What is involved in the construction and operation of an AC generator? How is electrical power transmitted across countries? What can we do to convert AC to DC? What is a capacitor?
Key Concepts
Electromagnetic induction is the process by which an EMF is induced due to the relative motion of a magnetic field and conductor.
Faraday's law and Lenz's law can be combined to determine the magnitude and direction of the induced EMF:
\(\varepsilon =-{\mathrm{d}N\Phi\over \mathrm{d}t}\)
- \(\varepsilon \) is the induced EMF (V)
- \(N\Phi\) is the magnetic flux linkage (Tm2 or Wb)
- \({\mathrm{d}N\Phi\over \mathrm{d}t}\) is the rate of change of magnetic flux linkage (Tm2s-1 or Wb s-1)
Construction
An AC generator consists of a rotating coil inside a magnetic field. The angle of the coil within the field affects the size and direction of the current induced; the current output is sinusoidal.
Induced current and EMF
To perform calculations with the induced current and EMF, root mean square quantities are used:
\(I_\text{rms}={I_0\over \sqrt2}\)
- \(I_\text{rms}\) is the root mean square current (A)
- \(I_0\) is the maximum magnitude of the current in either direction (A)
\(V_\text{rms}={V_0\over \sqrt2}\)
- \(V_\text{rms}\) is the root mean square potential difference (V)
- \(V_0\) is the maximum magnitude of the potential difference (V)
\(R={V_0\over I_0}={V_\text{rms}\over I_\text{rms}}\)
- \(R\) is the resistance (\(\Omega\))
\(P_\text{max}=I_0V_0\)
- \(P_\text{max}\) is the maximum power (W)
\(\bar{P}={1\over 2}I_0V_0\)
- \(\bar{P}\) is the average power (W)
AC generator equation
The size of the EMF induced varies according to the AC generator equation:
\(\varepsilon=BAN\omega \sin{\omega t}\)
- \(\varepsilon\) is the EMF at a given time (V)
- \(B\) is magnetic flux density (T)
- \(A\) is the perpendicular area of the coil in the field (m2)
- \(N\) is the number of turns on the coil
- \(\omega\) is angular velocity (rad s-1)
- \(t\) is time, with \(t=0\) for the coil sides rotating parallel to the field
Transformers are used in electrical power transmission to increase voltage and decrease current (step-up) or to decrease voltage (step-down). The nature of the transformer depends on the ratio of turns between the primary and secondary coils:
For an ideal transformer:
\({\varepsilon_p\over \varepsilon_s}={N_p\over N_s}={I_s\over I_p}\)
- \(\varepsilon_p\) is the EMF on the primary coil (V)
- \(\varepsilon_s\) is the EMF on the secondary coil (V)
- \(N_p\) is the number of turns on the primary coil
- \(N_s\) is the number of turns on the secondary coil
- \(I_s\) is the current in the secondary coil (A)
- \(I_p\) is the current in the primary coil (A)
Alternating current can be converted into direct current by rectification:
- In half wave rectification, a diode is inserted. Current will only pass in forward bias.
- In full wave rectification, two diode pathways are inserted. Current will pass in either direction, but will always enter the load resistor at the same side.
- The addition of a capacitor to a diode bridge rectification circuit creates a smoothing effect.
Diodes are made from semiconducting materials containing a p-n junction.
Capacitance
The capacitance of a capacitor is defined as the ratio of the charge stored to the potential difference across the capacitor:
\(C={q\over V}\)
- \(C\) is capacitance (F)
- \(q\) is charge (C)
- \(V\) is potential difference (V)
\(E={1\over 2}CV^2\)
- \(E\) is the energy stored on the capacitor or the work done that was required to store the charges (J)
Charging and discharging
Capacitors can be charged and discharged using a two-way switch circuit:
When discharging, the charge, current and potential difference decay exponentially over time:
\(q=q_0e^{-t\over \tau}\)
\(I=I_0e^{-t\over \tau}\)
\(V=V_0e^{-t\over \tau}\)
- \(q\) is the remaining charge stored on the capacitor (C)
- \(q_0\) is the initial charge stored on the capacitor (C)
- \(I\) is the current (A)
- \(I_0\) is the initial current (A)
- \(V\) is the potential difference across the capacitor (C)
- \(V_0\) is the initial potential difference across the capacitor (C)
- \(t\) is the time over which the capacitor has been discharging (s)
- \(\tau\) is the time constant (s)
How much of AHL EM induction have you understood?
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