In a parallel circuit, what happens to the voltage drop and current through the first resistor when a third resistor is added?

In a parallel circuit, each resistor shares the same voltage across it, which is equal to the voltage of the power supply. Therefore, when a third resistor is added in parallel with the existing resistors, the voltage drop across the first resistor remains unchanged because the voltage across all components in a parallel circuit is constant.

Regarding the current through the first resistor, while the total current drawn from the power source increases due to the addition of the new resistor (as there are now more paths for current to flow), the current through the first resistor remains unchanged because the voltage across it has not changed. The total current in the circuit is divided among all the available paths (the resistors), but this individual current through the first resistor does not increase or decrease due to the addition of another resistor.

Thus, in a parallel circuit, adding more resistors does not affect the voltage drop across existing resistors, nor does it affect their individual currents. This is why the choice that states nothing happens to the voltage drop and current is the correct answer.