The diode always wants to keep the required voltage for itself
So if you have a 1V supply, the diode will measure 0,7V and the resistor 0,3
5V would make the resistor measure 4,3V and the diode 0,7
To measure current in a circuit with a diode in series, you have to take out the 0,7V drop voltage from the input voltage in the formula I=U/R
Lets say your supply is 0,8V the resistor is 10ohm's and a diode in series the current is:
I=(U-0,7)/R
I=0,1/10
I=0,01A
So if you have a supply under 0,7V, youre gonna get very low or no current