A short circuit to the grounded metal case of an appliance occurs as shown in Figure 23.60. The person touching the case is wet and only has a 3.00 kΩ3.00\textrm{ k}\Omega resistance to earth/ ground. (a) What is the voltage on the case if 5.00 mA flows through the person? (b) What is the current in the short circuit if the resistance of the earth/ground wire is 0.200 Ω0.200\textrm{ }\Omega ? (c) Will this trigger the 20.0 A circuit breaker supplying the appliance?
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Final Answer
  1. 15.0 V15.0\textrm{ V}
  2. Yes, the circuit breaker will trip.

Solution video

OpenStax College Physics for AP® Courses, Chapter 23, Problem 54 (Problems & Exercises)

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Video Transcript
This is College Physics Answers with Shaun Dychko. This appliance has a short-circuit, which is to say that there's a wire that's accidentally touching the case of the appliance and there's a person also touching the case and the person provides a path to ground with a resistance of 3.00 kiloohms which is 3.00 times 10 to the 3 ohms and there's also a ground wire fortunately which takes most of the current directly to ground and that connection to ground here is 0.200 ohms resistance and the current flowing through the person is 5.00 milliamps, which is 5.00 times 10 to the minus 3 amps and question (a) asks what is the voltage of the case? So the voltage is current times resistance so that's 5.00 milliamps times 3.00 kiloohms and that's 15.0 volts. Part (b) asks will the circuit breaker—that's what CB stand for— will the circuit breaker be tripped by this short circuit? In other words, will there be enough current to exceed the 20.0 amp threshold for triggering this circuit breaker? So the ground and the person are connected in parallel to this case and the question is what is the total current through both of these branches and the current through the ground circuit is the voltage of the case divided by the ground resistance so that's 15.0 volts— that we found in part (a)— divided by 0.200 ohms which is 75.0 amps. So there's 75.0 amps going through this short-circuit... well, through the ground section here anyway but then you add that to the 5.00 milliamps through the person and it's still basically 75.0 amps. So the total current going through the circuit breaker is gonna be the current that's going through this short plus the current going through the appliance but we don't need to know what the current is through the appliance because the short is already taking 75.0 amps and that exceeds 20.0 amps needed to trick the circuit breaker and so yes, the circuit breaker will trip.