Voltage Drop
Despription and formulas of the voltage drop calculation
If several resistors are connected in series in a circuit, part of the total voltage drops across the individual resistors. This also applies to the connecting cable that connects the consumer to the voltage source.
The line resistance forms a series connection with the consumer. The voltage drop on the line that is lost to the consumer is called loss voltage.
\(loss\; voltage = current ยท wire\; resistance\)
\(U_V=I·R_L\)
The effective effective voltage at the consumer corresponds to the clamping voltage minus the voltage loss caused by the line resistance.
\(effective\; voltage = clamping \;voltage - voltage\; loss\)
\(\displaystyle U_N=U-U_V=U-I·R_L\)
According to the formula \(U_V=I·R_L\) the loss voltage depends on the current \(I\) and the line resistanced \(R_L\).
The line resistance is greater the longer the length \(l\) and the smaller the smaller the line cross section \(A\).
The line resistance is calculated using the formula
- for one wire length \(\displaystyle R_L=\frac{ρ·l}{A}\)
- for outgoing and return line \(\displaystyle R_L=\frac{ρ·2l}{A}\)
* \(ρ\) stands for the specific resistance of the line.
The loss voltage is calculated according to the formula
\(\displaystyle U_V=ρ· \frac{2·l·I}{A}\)
Example
In the following example, the loss voltage of a 50m long cable with a cross section of 2.5 mm2, a voltage of 230 volts and a current of 15 amperes.
\(\displaystyle U_V= ρ· \frac{2·l·I}{A} = 0.018 · \frac{2·50 ·15}{2.5}=10.8\; Volt\)
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