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Power lines basics
Electrical energy transmitted from power station along power lines (Aluminium).
Lines are engineered as excellent conductors but huge length involved means some resistance.
A current passing through a resistance will cause a power loss:
$$\begin{align}
P_{\text{loss}}=I^{2}R\ Js^{-1},W \\
\end{align}
$$
This loss comes in the form of primarily heat loss.
To minimise power loss, transmit power with as low a current as possible.
$$\begin{align}
P=VI
\end{align}
$$
- For the same power, lower current (to reduce $P_{\text{loss}}$), use a higher voltage.
- As $V \propto \frac{1}{I}$
Note that the voltage drop between two points is:
$$\begin{align}
V_{\text{drop}}=IR
\end{align}
$$
Farmhouse problem
- $2400W$ of power transmitted at $240V$ through resistance of $2\ohm$. What is the power loss?
$$\begin{align}
P_{\text{in}}=VI \therefore I_{\text{in}} = \frac{P}{V}=\frac{2400}{240}=10A \\
\therefore P_{\text{loss}}=I^{2}R=10^{2}\times2=200W\text{ lost} \\
\therefore P_{\text{out}}=P_{\text{in}}-P_{\text{loss}}=2200W \\ \\
V_{\text{drop}}=IR=10\times 2 = 20V \\
\therefore V_{\text{out}}=V_{\text{in}}-V_{\text{drop}}=240-20=220V \\
\therefore I_{\text{out}}=\frac{P_{\text{out}}}{V_{\text{out}}}=\frac{2200}{220}=10A \\
\text{Which should make sense, as current should be the same.}
\end{align}
$$
- Tip: don't use supply voltage everywhere! If you're doing that, you're probably doing something wrong.
- $2400W$ of power transmitted at $2400V$ through resistance of $2\ohm$. What is the power loss?
$$\begin{align}
P_{\text{in}}=VI \therefore I_{\text{in}}=\frac{P}{V}=\frac{2400}{2400}=1A \\
\therefore P_{\text{loss}}=I^{2}R=1^{2} \times 2=2W
\end{align}
$$
- This indicates that by increasing the voltage we can drastically reduce the power loss.
- In summary:
- Power from power plant is stepped up and transmitted over long distances
- This power is stepped down slightly at a substation found in your local area, so that it can be transmitted at lower distances without much danger.
- It is then stepped down again for consumer use.
