Failed Device - What Circuit Fault is Indicated and Where?

[mjcino]

1. The problem statement, all variables and given/known data
Four devices are connected in series across a voltage source of 120V. The total circuit current is 4.5A. One device fails to operate. The voltage across each of the other devices is 40V. What circuit fault is indicated and where?


2. Relevant equations
E=IR
I=E/R
R=E/I
et al.


3. The attempt at a solution
I'm afraid I'm not really sure what the instructor is looking for here. It seems clear to me that one of the devices has shorted out. I wrote for my answer, "One of the devices has shorted out - its resistance has become 0 ohms." That sounds like the circuit fault to me, but where . . . ? Am I missing something here?

[vk6kro]

I think you have it right.

If there were only resistive devices present, (ie no inductors or capacitors) the total resistance is 26.66 ohms ( 120 V / 4.5 Amps = 26.66 ohms.) Each device has 40 volts across it and 4.5 amps through it, so each has a resistance of 8.89 ohms. ( 40 V / 4.5 = 8.89 ohms).

The main clue is that the 3 remaining devices have a total of 120 volts across them, so there can't be any voltage across the remaining device, whatever it was.
Maybe this indicates a fault. Maybe not. You would have to know what the other device was.

Unless you are told that this was a fault, the 4th device could be a switch. It is quite normal for a switch to be short-circuited when it is turned on.

[berkeman]

1. The problem statement, all variables and given/known data
Four devices are connected in series across a voltage source of 120V. The total circuit current is 4.5A. One device fails to operate. The voltage across each of the other devices is 40V. What circuit fault is indicated and where?


2. Relevant equations
E=IR
I=E/R
R=E/I
et al.


3. The attempt at a solution
I'm afraid I'm not really sure what the instructor is looking for here. It seems clear to me that one of the devices has shorted out. I wrote for my answer, "One of the devices has shorted out - its resistance has become 0 ohms." That sounds like the circuit fault to me, but where . . . ? Am I missing something here?

I agree with v6kro. The only thing I can add is that it is common in talking about failures of electronic devices to classify them as failed short or failed open. And it is also common for a device to first fail short, and then fail open as it dissipates too much power and overheats to the point of melting and blowing open.