Water heater should be set in a drip pan.
Otherwise, put 1 gallon bucket under TP release pipe to catch water.http://waterheatertimer.org/Water-at-bottom-of-water-heater.html#drip-pan
When you say relief valve, I assum you are talking about brass valve located on top of tank or near top of tank. This is TP valve and a pipe connects to this valve and runs down to within 6" of bottom of tank. TP valve has a small lever on it.
If you are talking about tank drain valve located at bottom of tank, then add a comment.
Following information is for TP valve.
Dripping TP valve can be caused by 3 different thing:
1) Obstruction inside TP valve. Open TP valve for a moment to flush away
particles and slowly lower lever back down. See if water stops
dripping, if not, then replace TP valve
2) Defective TP valve: replace TP valve. Turn off electricity to water heater. Let heater cool for several hours so you do not get scalded. Close shut off valve located above tank on cold side. Open tub spout to relieve pressure, open tank drain or open TP valve and empty water below TP valve level. If TP is located on top of tank, not much water has to be drained. Tank is under press when hot, so be careful. Put teflon tape on new valve and install with big pipe wrench by turning clockwise until TP valve is very tight.
3) Overheating tank. TP valve is temperature-pressure valve. If tank water is over 150 degrees, the TP valve starts drizzling hot water to relieve tank pressure.
Lower tank pressure two different ways:
a) turn down thermostathttp://waterheatertimer.org/How-to-adjust-water-heater-temperature.html
b) install expansion tank on incoming cold water linehttp://waterheatertimer.org/Water-at-bottom-of-water-heater.html#expansion-tank