You have a bad connection somewhere in the circuit. You'll have to pull apart the various junctions (outlets, switches, and fixtures) on this circuit to isolate the issue.
With the power turned off, disconnect the circuit somewhere that you suspect the issue to be located (unhook the load wires that go to the next junction). Outlets on the load side of that junction won't have any voltage when you turn the power back on. If the junction your testing had a low voltage issue, then you know that the issue isn't with any outlets that have no power with the load side disconnected. And if the junction your testing had the proper voltage, then the problem won't be with any junctions that still have power with the load side disconnected. Use this process of elimination to quickly narrow down which junctions could have a faulty connection.
You're simply trying to narrow down the problem in this chain, so here's an example:
breaker ---1---2---3---4X---5---6---7---
In the above, the numbers are your junctions on the circuit, and the X is your fault. Then:
- 3 won't have any voltage issues and if you disconnect it, 1 and 2 will still be live so they're eliminated and you'll know the problem is with junctions 3 through 7.
- 5 will have issues and if you disconnect it, 6 and 7 will lose power, so now you know that 6 and 7 are eliminated and the issue is with junctions 3 through 5.
- assume 4 doesn't have issues, and when you disconnect it, you see 5 lose power. Now you know that 3 is not an issue and your left with the wire between 4 and 5 or in one of those junction boxes.
The trick is that your junctions won't be numbered, so you just have to keep track of what works and what doesn't with each test. A sensitive non-contact voltage tester or stud finder with voltage sensitivity can help with tracing the circuit to find the most likely places for the bad connection.
As Tester101 would say, if you're at all uncertain, this is a good point for an electrician to help. One bad connection could indicate a lot of other issues from poor workmanship, and these issues are potential fire or electrocution hazards.
Best Answer
You have bad wiring or a bad outlet. Turn off the breaker for that circuit immediately as this type of problem can cause arcing or heating at the site of the break, possibly leading to a fire. And no, this type of failure may not trip a breaker.
Depending on your comfort working with household voltages and wiring, you can start troubleshooting by figuring out where the wire for those outlets start and inspecting the end for corrosion, nicks on the conductor, or breaks in the conductor or insulation. Also try replacing the outlets themselves, including the outlet before the non-working outlets.
A quick anecdote: an outlet in my previous house that had been working fine for years developed this weird behavior where if something was plugged in, nothing else in the room worked. Turns out that the outlet had a manufacturing defect that only became apparent after 4 years of use.