In a parallel circuit, the current through a branch is inversely proportional to the branch's resistance.

In a parallel circuit, the current through a branch is inversely proportional to the branch's resistance.

• A. Directly proportional
• B. Proportional to voltage
• C. Proportional to power
• D. Inversely proportional

Answer: (D)

In a parallel circuit, each branch has the same voltage across it, so Ohm’s law applies to each branch: I = V / R. With the voltage fixed, the current through a branch is determined by the branch’s resistance, and it decreases as resistance increases. This is an inverse relationship: doubling the resistance makes the current roughly half as large. That’s why the current through a branch is inversely proportional to the branch’s resistance. Direct proportionality would imply higher resistance yields more current, which isn’t true here. Current is indeed proportional to voltage for a given resistance, but the statement focuses on how current varies with resistance at the same voltage. Power relationships exist (P = V^2 / R or P = I^2 R), but they don’t describe the primary dependence of current on resistance in a parallel branch.

In a parallel circuit, each branch has the same voltage across it, so Ohm’s law applies to each branch: I = V / R. With the voltage fixed, the current through a branch is determined by the branch’s resistance, and it decreases as resistance increases. This is an inverse relationship: doubling the resistance makes the current roughly half as large. That’s why the current through a branch is inversely proportional to the branch’s resistance.

Direct proportionality would imply higher resistance yields more current, which isn’t true here. Current is indeed proportional to voltage for a given resistance, but the statement focuses on how current varies with resistance at the same voltage. Power relationships exist (P = V^2 / R or P = I^2 R), but they don’t describe the primary dependence of current on resistance in a parallel branch.