Calculation gives negative current I am trying to learn how to analyse very simple circuits. As a first step I assume a direction for the current. If my analysis gives a negative value for current, then I have chosen the wrong direction. If I continue to analyse the circuit, then the potential across a resistor will appear to increase. This suggests a gain in energy from the resistor which can’t happen? 
In the event that I find a negative value for current should I restart the calculation with the current in the correct direction? 
 A: 
As a first step I assume a direction for the current. If my analysis
  gives a negative value for current, then I have chosen the wrong
  direction.

No, it's not possible to choose the wrong direction since you don't assume a direction for the current, you assume a reference direction which is essentially the physical equivalent of choosing where to place the red (positive) lead of one's ammeter.
(Here I assume a DC circuit context).
If one connects an ammeter in series with a resistor, one may read either a positive or negative value.
If another connects an ammeter in series with yours but with the opposite polarity, their ammeter will read the opposite sign as yours.
And yet, both ammeters give precisely the same information, i.e., the actual direction of the current.
Equivalently, if you choose one reference direction and you (correctly) calculate a negative value while another student chooses the opposite reference direction and calculates a positive current of the same magnitude, both answers are equivalent and correct.
A: Potential drop across the resistor will be -IR if you move in the direction of current from a higher potential to a lower potential. In the same circuit (with the same direction of current), if you wish to go the other way around then the potential drop will be +IR when you go from a lower potential to a higher potential.
Potential drop is the potential difference across the resistor = $V_{final} - V_{initial}$. High to low gives $-ve$ potential difference and low to high gives $+ve$ potential difference. 
When calculating the current, do the standard calculations by assuming the direction of current and the potential drops across resistors according to this assumption. All the value of the potential drops in the complete circuit according to this assumption will be equated to zero. If you multiply both sides by $-1$ you will still get the same answer but the directions of the currents (or potential drops) will be in the opposite direction.
If you get $-ve$ value of current then the direction of current will be opposite to the direction of the current that you assumed.
