Two identical resistors are connected in parallel across the terminals of an ideal battery. If the resistance of one of them is increased, what happens to the current through, and the voltage across, the OTHER resistor?

1. In a parallel connection, both ends of every resistor are tied to the same two wires, which connect straight to the battery's terminals. 2. An ideal battery holds a fixed voltage across those two terminals no matter what happens elsewhere in the circuit. 3. The voltage across the untouched resistor is therefore still fixed at the battery voltage, unchanged by the other resistor's new value. 4. The untouched resistor's own resistance has not changed either. 5. By Ohm's law, I = V/R for that resistor, and since both V and R are unchanged for it, its current is also unchanged. 6. This is a trap that catches students who assume changing 'the total resistance' must change every current in the circuit; in an ideal parallel network, one branch is isolated from changes in the others. 7. So both the current through, and the voltage across, the other resistor remain exactly the same. _Source: OpenStax Physics (CC BY 4.0), Ch 19 "Electrical Circuits", section 19.3 Parallel Circuits_