At the terminals of a receiver with a resistance of 4 Ω is installed a source with an internal resistance of 0.2 Ω and EMF (electromotive force) of 150 V. The connecting wires have a resistance of 0.4 Ω. What is the voltage drop on the supply line and what is the voltage at the terminals?
R (resistance) = 4 Ω
r (internal resistance) = 0.2 Ω
E (EMF) = 150 V
EMF = Electromotive Force
R' (connection conductive resistance) = 0.4 Ω
i (current intensity) = ?
UAB (voltage at the receiver terminals) = ?
UCD (voltage across resistor R) = ?
Uline (voltage drop on the supply line) = ?
At the terminals of a receiver with a resistance of 4 Ω, an electrical source with an internal resistance of 0.2 Ω and EMF (electromotive force) of 150 V
Solution:
$$E = i(2R' + R + r)$$
$$i = frac{E}{2R' + R + r}$$
$$UAB = E - ir$$
$$UCD = i \cdot R$$
$$ULine = 2 \cdot R' \cdot i$$
We replace the values in the formulas:
$$R = 4 \ Ω$$
$$r = 0.2 \ Ω$$
$$E = 150 \ V$$
$$R' = 0.4 \ Ω$$
We calculate i:
$$i = \frac{E}{2R' + R + r}$$
$$i = \frac{150}{2 \cdot 0.4 + 4 + 0.2}$$
$$i = \frac{150}{0.8 + 4 + 0.2}$$
$$i = \frac{150}{5}$$
$$i = 30 \ A$$
We calculate UAB:
$$UAB = E - ir$$
$$UAB = 150 - (30 \cdot 0.2)$$
$$UAB = 150 - 6$$
$$UAB = 144 \ V$$
We calculate UCD:
$$UCD = i \cdot R$$
$$UCD = 30 \cdot 4$$
$$UCD = 120 \ V$$
We calculate Uline:
$$Uline = 2 \cdot R' \cdot i$$
$$Uline = 2 \cdot 0.4 \cdot 30$$
$$Uline = 24 \ V$$
Thus, the voltage drop on the supply line (Uline) is 24 V, the voltage at the receiver terminals (UAB) is 144 V, and the voltage between the ends of the resistor R (UCD) is 120 V.
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