Sounds like you might have a thermostat problem, or burned out lower element
Lower thermostat and both elements will test for 120V at all times because upper thermostat only cuts off one leg of 240V circuit, and other leg is hot all the time.http://waterheatertimer.org/How-to-test-water-heater-element.htmlhttp://waterheatertimer.org/How-water-heater-thermostat-works.htmlhttp://waterheatertimer.org/How-to-wire-water-heater-thermostats.htmlhttp://waterheatertimer.org/How-to-replace-thermostat-on-electric-water-heater.html
Yes, the elements alternate being turned ON.
This is called non-simultaneous operation.
Look at label on side of tank: Each element has rating of 4500Watts, but tank rating is also 4500Watts > that shows that both elements are not ON at same time.
This is standard wiring for water heaters.
Water heaters can we wired differently, for example converted to simultaneous operation where upper thermostat and lower thermostat are no longer wired together, so upper and lower parts of tank are independent.
Lower thermostat is replaced with ECO protected thermostat identical to upper thermostat.
Another 240V circuit breaker is added to breaker panel, and that 240V line runs directly to lower thermostat. So upper and lower thermostats are each on separate 240V line.
The advantage of simultaneous is faster recovery of hot water, but downside is probably higher electric bill. Simultaneous wiring is usually reserved for larger tanks like 80 gallons, where elements can fall behind the amount of hot water needed.
Otherwise, ordinary non-simultaneous operation is proven to be satisfactory, if your home has not experienced shortages.http://waterheatertimer.org/B220C.htmlhttp://waterheatertimer.org/How-to-wire-off-peak-water-heater-thermostats.htmlhttp://waterheatertimer.org/Do-it-yourself-water-heater-timer.html
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