If the current source is closed to a resistor with a resistance of R1 = 4 Ohm, then the current in the circuit I1 = 0.2 A.

If the current source is closed to a resistor with a resistance of R1 = 4 Ohm, then the current in the circuit I1 = 0.2 A. If the resistor is replaced with another resistance R2 = 7 Ohm, the current in the circuit I2 = 0.14 A. Determine the short-circuit current …

To determine the current strength I in a circuit with a load resistance R, we use Ohm’s law for a complete circuit: I = E / (R + r), where E is the EMF of the current source, r is the internal resistance of the current source. If the current source is closed to a resistor with a resistance of R₁ = 4 Ohm, then the current in the circuit will be I₁ = 0.2 A, then I₁ = E / (R₁ + r) and r = E / I₁ – R₁. If the resistor is replaced with another, with resistance R₂ = 7 Ohm, the current in the circuit is I₂ = 0.14 A, we get I₂ = E / (R₂ + r) and r = E / I₂ – R₂. Hence, E / I₁ – R₁ = E / I₂ – R₂. Hence:

Е = I₁ ∙ I₂ ∙ (R₁ – R₂): (I₂ – I₁) or

E = 0.2 A ∙ 0.14 A ∙ (4 Ohm – 7 Ohm) / (0.14 A – 0.2 A);

E = 1.4 V;

r = 1.4 V / 0.2 A – 4 ohms;

r = 3 ohms.

To determine the short-circuit current strength, we find the ratio:

Ikz = E / r or

Isc = 1.4 V / 3 Ohm;

Isc = 0.47 A.

Answer: the short-circuit current is 0.47 A.