2 how are fields used to move electrical energy
2.1 electromagnetic induction
| name | symbol | units |
|---|---|---|
| magnetic flux | \(\Phi\) | \((Wb)\) |
| magnetic field strength | \(B\) | \((T)\) |
| area of loop | \(A\) | \((m^2)\) |
| electromotive force (EMF) | \(\varepsilon\) | \((V)\) |
| length of wire | \(l\) | \((m)\) |
| velocity of wire | \(v\) | \((ms^-1)\) |
2.1.1 magnetic flux
magnetic flux is the number of magnetic field lines passing through a surface (such as a loop of wire)
\[\Phi=B_\perp{A}\]
2.1.2 faraday’s law
faraday’s law states that an EMF is generated in a current carrying loop equal to the negative rate of change of magnetic flux
rotating loop in a magnetic field
\[\varepsilon=n\frac{\Delta{\Phi}}{\Delta{t}}\]
wire moving in a magnetic field
\[\varepsilon=Blv\]
2.1.3 lenz’s law
lenz’s law states that the direction of the induced current is such that the magnetic field of the current opposes the direction of the change in magnetic field.
2.1.4 slip ring
slip ring is used to connect the loop to the rest of the circuit resulting in a continuous AC (alternating current)
2.1.5 split ring
split ring commutator** reverses the direction of the current every half turn, flipping all the negative currents into positive currents making DC (direct current)
2.1.6 RMS voltage
RMS voltage is the equivalent DC voltage that produces the same power in a load as the corresponding AC voltage
\[V_{RMS}=\frac{V_{peak}}{\sqrt{2}}\]
\[I_{RMS}=\frac{I_{peak}}{\sqrt{2}}\]
2.2 power transmission
| name | symbol | units |
|---|---|---|
| power | \(P\) | \((W)\) |
| voltage | \(V\) | \((V)\) |
| current | \(I\) | \((A)\) |
| number of loops | \(n\) | |
| resistance | \(R\) | \((\Omega)\) |
2.2.1 power
\[P=VI\]
2.2.2 transformers
transformers is used to increase/decrease the voltage in a current to reduce power loss when transmitting power and it only works with AC Current.
\[P_\text{in}=P_\text{out}\] \[V_{p}I_{p}=V_{s}I_{s}\] \[\frac{I_s}{I_p}=\frac{V_p}{V_s}=\frac{n_p}{n_s}\]
2.2.3 ohms Law
\[V=IR\]
2.2.4 power loss
\[P_{\text{loss}}=I_\text{line}^2R_\text{line}\]
2.2.5 voltage drop
\[V_\text{supply}=V_\text{load}+V_\text{drop}\] \[V_\text{drop}=I_\text{line}R_\text{line}\]