When a closed switch provides an ideal wire path around a resistor, both ends of that resistor are at the same potential. There is zero potential difference across it, so no current flows through that resistor in the ideal circuit.
The other series resistor remains in the circuit. Removing one resistor from the effective current path lowers the total resistance, so an ideal fixed-voltage supply delivers more current.
- Trace the path from one battery terminal to the other.
- Mark any two points joined by an ideal wire as having the same potential.
- Recalculate the total resistance after the switch closes.
Worked example | Two 6 Ω resistors and a 12 V supply
A 12 V ideal supply is connected to two 6 Ω resistors in series. A switch is connected directly across the second resistor. When the switch is open, the total resistance is 12 Ω and the current is 12 ÷ 12 = 1 A through both resistors. Each has a potential difference of 6 V.
Close the switch. The second resistor now has a wire path across it, so its potential difference becomes 0 V. The first resistor is still in the main loop, so total resistance falls to 6 Ω. The supply current is now 2 A and all 12 V is across the first resistor.
Check exactly what the switch connects
Look at the two nodes joined by the switch. In this circuit they are the ends of the second resistor, so only that resistor is bypassed. The first resistor still limits the supply current.
A switch in series with both resistors would act differently. Opening it would break the main loop. Closing it would restore the two-resistor path.
Try a pair of unequal resistors
A 3 Ω resistor and a 9 Ω resistor are in series across an ideal 12 V supply. Closing a switch bypasses the 9 Ω resistor. Find the current through the 3 Ω resistor before and after closing.
Answer. Before closing, the current is 12 ÷ (3 + 9) = 1 A. After closing, it is 12 ÷ 3 = 4 A.
Frequently asked questions
Why is the potential difference across the bypassed resistor zero?
The ideal closed switch and connecting wire join both ends at the same potential.
Is the whole supply short-circuited?
The remaining resistor is still between the supply terminals and limits the current. A wire directly across the supply terminals would be a different circuit.
Official information
SEAB, 2027 SEC G3 Physics syllabus (K323), D.C. Circuits. Syllabus checked 11 November 2026. The examples are original.