Final answer:
Adding a resistor can either increase or decrease the current, depending on how it's added to the circuit. Resistors added in series increase the total resistance and decrease current, while resistors added in parallel decrease the total resistance and increase current.
Step-by-step explanation:
The statement that 'adding a resistor increases current' is actually misleading, as this is only true under specific circumstances, namely when resistors are added in parallel.
Normally, adding a resistor in series with others in a circuit will increase the total resistance and decrease the current according to Ohm's law.
However, when resistors are added in parallel, the total resistance of the circuit decreases.
Consider this analogy: the current in an electrical circuit is similar to water flowing through pipes. When you provide more paths by adding pipes in parallel, the water can flow more easily, which in this case means the overall resistance decreases, allowing more current to flow through the circuit. This is why, when resistors are added in parallel, the current in the circuit can increase due to the decrease in total resistance.
For instance, if three identical resistors R are added in parallel, they make three identical paths for the current. This makes it effectively three times easier for the current to flow compared to just a single resistor. Thus, the total resistance is lowered, and more current can flow throughout the circuit.
So, to clarify: adding resistors in series increases resistance and decreases current, while adding resistors in parallel decreases resistance and increases current.