Submersible Motor control Capacitor replacement

The other day, we had no water pressure in our house. We are on a well and use a submersible water pump coupled to a pressure tank to provide all the houses water needs.
First, I checked the pressure switch. All checked out OK.
Next test was the motor control box.
Opening it up and inspecting the capacitor, the relay and the wiring, everything looked OK as well.
Not knowing how to test these components, I just went to another well (with identical components) we have on the property and took off the motor control cover and inserted it on the house control box. Turned the power back on and presto! We now have water again.

So that's the backstory.
I did some research into how to test these components to see if it can be repaired rather than just throwing it away and buying a new one.  
I found some you tube videos on how to test the relay which was straight forward and simple. All tests passed.
The capacitor on the other hand is a little more tricky. I don't have the type of multimeter to test capacitance so I'm just relying on that disk to be bulged or any leaks that I see. Both didn't have these symptoms.
In the photo I took of ours, the disk is not bulged but is black. All the pictures I see on the internet are white and say mostly that it turns yellow when its blown.
Also, ours has a resistor that looks a little suspiciously burnt at the one end as well.
Most capacitors that I see on the internet don't even have a resistor. Why does mine have one?
Any thoughts or help are appreciated.

That is called a bleeder resistor. It's purpose is to bleed off the charge on the capacitor to avoid shocking someone. The capacitor is rated at 270 volts so that's quite a potential zap. The resistor might be ok but it looks like it needs to be replaced. The color bands identify the resistor value but the pic is not clear enough to accurately determine. The resistor color code is available online.

A capacitor can be checked with a standard multimeter but it's a bit tricky & not a very reliable test. Electrolytics are known to go bad fairly often, compared to other type of caps. Since you replaced the cap & the pump started working it's a safe bet that it's defective.

That's good information about the resistor I didn't know. Thanks for that Mike!

So I assume whether the resistor is working or not, it shouldn't affect whether the capacitor works.

I am also assuming that a black tab indicates the cap is bad also.

The resistor can be removed without affecting the function of the capacitor. Just beware that the cap will then hold a potential voltage of 270 x 1.414 = 380 volts peak. (it's an AC/DC conversion thing)

I hate to speculate on the black cap. That's not a normal thing for most electrolytics to have.

I build and repair a lot of electronics, Ham/CB radios mostly. Anyways, I bought a capacitance tester off amazon for I think $20, maybe. But if you aren't going to check a bunch you can just part swap to see what works.

Just received my new capacitor in the mail. Installed it and works great.

Also, the small tab on the end is white. So its true that when it turns black, its bad.

In the future a microFarad test needs to read 86 +20% -0% that will show whether it is good or bad, option on most decent multimeters

Gerry Parent wrote:The other day, we had no water pressure in our house. We are on a well and use a submersible water pump coupled to a pressure tank to provide all the houses water needs.

We have a very similar system. Until recently we had no problems with the water, and then, one morning, no water. I did all the same checks with nothing visibly wrong. Turned the power back on to the system and away it went. Had this happen several times and it was a puzzle until I realised it coincided with the filter backwash, which happens every ten days. I've found that if we run the dishwasher or washing machine in the evening before the backwash is due then we'll have no water in the morning. If I turn the power off for a while it starts again happily. There seems to be a low water cut out which needs a power cut before resetting itself.
If be interested to hear if anyone else has similar happenings.

Chances are the backwash function is draining the line at some point. If there is a power interruption, like a power overload on the circuit by running other appliances, then if the pump is not self priming, it will fail to function.