With an external resistance of 20 ohms, the potential difference across the source terminals is 30 V

| March 26, 2021 | education

With an external resistance of 20 ohms, the potential difference across the source terminals is 30 V, with a resistance of 40 ohms, the current is 1 A. Determine the internal resistance of the source?

R1 = 20 ohms.

U1 = 30 V.

R2 = 40 ohms.

I2 = 1 A.

r -?

Let’s write Ohm’s law for a section of a circuit and for a closed loop for the first resistance: I1 = U1 / R1, I1 = EMF / (R1 + r).

U1 / R1 = EMF / (R1 + r).

EMF = (R1 + r) * U1 / R1.

For the second resistance, Ohm’s laws will have the form: I2 = U2 / R2, I2 = EMF / (R2 + r).

EMF = I2 * (R2 + r).

(R1 + r) * U1 / R1 = I2 * (R2 + r).

R1 * U1 + r * U1 = I2 * R2 * R1 + I2 * r * R1.

R1 * U1 – I2 * R2 * R1 = I2 * r * R1 – r * U1.

r = (R1 * U1 – I2 * R2 * R1) / (I2 * R1 – U1).

r = (20 Ohm * 30 V – 1 A * 40 Ohm * 20 Ohm) / (1 A * 20 Ohm – 30 V) = 20 Ohm.

Answer: the internal resistance of the current source is r = 20 ohms.



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