In a parallel circuit, if one branch has infinite resistance (an open circuit), what happens to the equivalent resistance of the network?

In a parallel circuit, if one branch has infinite resistance (an open circuit), what happens to the equivalent resistance of the network?

• A. The equivalent resistance increases without bound
• B. The circuit stops conducting entirely
• C. The open branch contributes no current; the equivalent resistance is determined by the other branches
• D. The equivalent resistance becomes zero

Answer: (C)

In a parallel circuit, the total resistance comes from the sum of the conductances (the reciprocals of the resistances) of each branch. An open branch has infinite resistance, so its conductance is zero and it contributes nothing to that sum. That means the equivalent resistance is determined entirely by the other, finite-resistance branches. The open path carries no current, and the network behaves as if that branch weren’t there, with the overall resistance equal to the parallel combination of the remaining branches. The circuit can still conduct through the other paths; it doesn’t become infinite or zero just because one branch is open.

In a parallel circuit, the total resistance comes from the sum of the conductances (the reciprocals of the resistances) of each branch. An open branch has infinite resistance, so its conductance is zero and it contributes nothing to that sum. That means the equivalent resistance is determined entirely by the other, finite-resistance branches. The open path carries no current, and the network behaves as if that branch weren’t there, with the overall resistance equal to the parallel combination of the remaining branches. The circuit can still conduct through the other paths; it doesn’t become infinite or zero just because one branch is open.