In parallel circuits, which statement is true?

In parallel circuits, which statement is true?

• A. In parallel circuits, currents are equal; 1/R_eq = 1/R1 + 1/R2.
• B. In parallel circuits, voltages are not equal.
• C. In parallel circuits, voltages are equal; 1/R_eq = 1/R1 + 1/R2.
• D. In parallel circuits, current is independent of resistance.

Answer: (C)

In parallel circuits, the same voltage appears across every path, because all branches are connected directly to the same two nodes. That means the potential difference across each branch is equal to the source voltage. The current in each branch follows Ohm’s law: I = V/R, so branches with smaller resistance draw more current. The total current is the sum of the branch currents, and the effective or equivalent resistance of the network is found using the reciprocal rule: 1/R_eq = 1/R1 + 1/R2 (and continues for more branches). So the statement that voltages are equal across all branches and that 1/R_eq = 1/R1 + 1/R2 describes how parallel circuits behave. The other options contradict how parallel circuits distribute current or voltage: currents are not generally equal, voltages are indeed equal across branches, and current depends on the resistance (per Ohm’s law).

In parallel circuits, the same voltage appears across every path, because all branches are connected directly to the same two nodes. That means the potential difference across each branch is equal to the source voltage. The current in each branch follows Ohm’s law: I = V/R, so branches with smaller resistance draw more current. The total current is the sum of the branch currents, and the effective or equivalent resistance of the network is found using the reciprocal rule: 1/R_eq = 1/R1 + 1/R2 (and continues for more branches).

So the statement that voltages are equal across all branches and that 1/R_eq = 1/R1 + 1/R2 describes how parallel circuits behave. The other options contradict how parallel circuits distribute current or voltage: currents are not generally equal, voltages are indeed equal across branches, and current depends on the resistance (per Ohm’s law).