(a) Find the terminal voltage of a 12.0-V motorcycle battery having a 0.600Ω0.600 \Omega internal resistance, if it is being charged by a current of 10.0 A. (b) What is the output voltage of the battery charger?
Question by OpenStax is licensed under CC BY 4.0
Final Answer
  1. 18.0 V18.0 \textrm{ V}
  2. 18.0 V18.0 \textrm{ V}

Solution video

OpenStax College Physics for AP® Courses, Chapter 21, Problem 19 (Problems & Exercises)

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Video Transcript
This is College Physics Answers with Shaun Dychko. We have a motorcycle battery with an EMF and an internal resistance connected to a charger which will draw as an EMF with a polarity opposite to that of the EMF battery. So we’re having the positive end of the charger connected to the positive end of the battery. And it’s going to cause the current to go this direction which is a bit unusual. And normally when we have batteries drawn like this, we have current going out of the positive end of the battery. But this charger has a greater voltage than that of the battery. And so it causes the current to go in the battery in the reversed direction than it normally does. And this is why it gets charged. And it has chemistry inside that will go in the reverse direction, when the current goes through the battery in the reverse direction. So the products of the chemistry when a battery is providing power become the reactants. And turn back into the original materials that they were. If it’s a LED acid battery, this current going through the battery in the opposite direction is going to create the LED again that was consumed in the reaction to begin with. Anyway, with the terminal voltage, we want to know what is the voltage from here to here. And so we go and we traverse in this direction. But we have a current going down through this internal resistance. And so, when we traverse in the upwards direction, and we go across the resistance in the opposite direction to the current, this is going to be a positive potential difference. And so we have the 12 Volts of the EMF and then we’re going to add to that. The potential difference across the resistor given that we’re traversing in the upwards direction, the opposite direction to the current which is going down. And so we have the terminal voltage and it’s 12 Volts plus ten Amps multiplied by the internal resistance of 0.6 Ohms giving us 18.0 Volts. And now in part b it asks what is the voltage of the charger, but the charger is connected between here and here. And so the charger voltage is the same as the terminal voltage. And it is 18.0 Volts.