EMF of the current source is 2V, internal resistance is 1 Ohm. Determine the resistance of the external

EMF of the current source is 2V, internal resistance is 1 Ohm. Determine the resistance of the external circuit if 0.75W of power is released in it.

Let us derive the formula for the power of the external circuit.

Circuit current

I = E / (R + r).

Dedicated power

P = U * I.

Voltage

U = I * I.

Replace and get the expression for the power on the external circuit

P = I² * R = (E / (R + r)) ² * R = E² * R / (R + r) ².

We substitute the known ones and calculate

0.75 = 2² * R / (R + 1) ²;

0.75 = 4R / (R² + 2R + 1);

4R = 0.75 * R² + 1.5 * R + 0.75;

3R² – 10R + 3 = 0;

D = 25 – 9 = 16.

The determinant is greater than zero, there are two roots

R1 = (5 – 4) / 3 = 0.33;

R2 = (5 + 4) / 3 = 3.

Answer: 0.33 ohm; 3 ohm.