The short-circuit current of the source Ik = 48 A. When a resistor with a resistance of R-19.5 Ohm is connected to the source

| April 11, 2021 | education

The short-circuit current of the source Ik = 48 A. When a resistor with a resistance of R-19.5 Ohm is connected to the source, the current I in the circuit has decreased to 1.2 A. Determine the EMF of the source and its internal resistance.

Ik = 48 A.

R = 19.5 ohms.

I = 1.2 A.

EMF -?

r -?

A short circuit is a circuit state in which there is no external resistance R = 0, the current reaches the maximum possible value.

Ohm’s law for a closed loop in a short circuit has the form: Ik = EMF / r, where EMF is the electromotive force of the current source, r is the internal resistance of the current source.

EMF = Ik * r.

Ohm’s law for a closed circuit is: I = EMF / (R + r), where I is the current in the circuit, R is the external resistance of the circuit.

EMF = I * (R + r).

Ik * r = I * (R + r).

Ik * r = I * R + I * r.

r = I * R / (Ik – I).

r = 1.2 A * 19.5 Ohm / (48 A – 1.2 A) = 0.5 Ohm.

EMF = 48 A * 0.5 Ohm = 24 V.

Answer: the current source has an EMF = 24 V and an internal resistance r = 0.5 Ohm.



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