Question

What happens to the current in a circuit if the resistance triples? If the voltage triples?

Answer 1

(Example 1 ) 
If the Voltage that furnishes the current is an ideal (no internal resistance) Voltage source. Then; 

V/R = i 
V/2R = i/2 If external resistance doubles, current reduced to 1/2 of original value 
V/3R = i/3 If external resistance triples, current reduced to 1/3 of original value 

(Example 2) 
But if the Voltage that furnishes the current is a practical [contains an internal resistance (Ri)] Voltage source. Then the current is a function of the Voltage source`s internal resistance, which does not double nor triple, plus the external resistance which is being doubled and tripled. 

V/(R + Ri) = i 
V/(2R + Ri) = greater than i/2 but less than I. 
V/(3R + Ri) = greater than i/3 but less than i/2