Find the EMF and the internal resistance of the galvanic cell, if the current is 0.6A

| May 22, 2021 | education

Find the EMF and the internal resistance of the galvanic cell, if the current is 0.6A with the resistance of the external circuit of 2 Ohm, and the current is 1A with the resistance of 1 Ohm.

R1 = 2 ohms.

I1 = 0.6 A.

R2 = 1 ohm.

I2 = 1 A.

r -?

EMF -?

Let us write Ohm’s law for a closed loop: I = EMF / (R + r), where I is the current in the circuit, EMF is the electromotive force of the current source, R is the external resistance of the circuit, r is the internal resistance of the current source.

I1 = EMF / (R1 + r).

EMF = I1 * (R1 + r).

I2 = EMF / (R2 + r).

EMF = I2 * (R2 + r).

I1 * (R1 + r) = I2 * (R2 + r).

I1 * R1 + I1 * r = I2 * R2 + I2 * r.

I1 * R1 – I2 * R2 = I2 * r – I1 * r.

We find the internal resistance of the current source by the formula: r = (I1 * R1 – I2 * R2) / (I2 – I1).

r = (0.6 A * 2 Ohm – 1 A * 1 Ohm) / (1 A – 0.6 A) = 0.5 Ohm.

EMF = 0.6 A * (2 Ohm + 0.5 Ohm) = 1.5 V.

Answer: r = 0.5 Ohm, EMF = 1.5 V.



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