In a parallel circuit, which statement is true?

In a parallel circuit, which statement is true?

• A. The current through each component is the same.
• B. The total resistance is the sum of the resistances.
• C. The voltage across each component is the same and conductances add.
• D. The power dissipated is the same for all branches.

Answer: (C)

In a parallel circuit, all branches share the same voltage because they are connected across the same two nodes. The current splits among the branches according to each branch’s resistance, so currents are not necessarily equal. The statement that the voltage across each component is the same and conductances add is correct. Across parallel branches, the same voltage appears on every path, and the total conductance is the sum of the individual branch conductances (so 1/R_total = Σ(1/R_i)). Why the others don’t fit: the current through each component in parallel isn’t the same—it depends on that branch’s resistance. The total resistance in parallel isn’t the sum of the resistances; it follows the reciprocal rule (the reciprocal of the total equals the sum of reciprocals). And the power dissipated in each branch isn’t necessarily identical; with the same voltage across branches, P_i = V^2 / R_i, so different R_i produce different powers.

In a parallel circuit, all branches share the same voltage because they are connected across the same two nodes. The current splits among the branches according to each branch’s resistance, so currents are not necessarily equal.

The statement that the voltage across each component is the same and conductances add is correct. Across parallel branches, the same voltage appears on every path, and the total conductance is the sum of the individual branch conductances (so 1/R_total = Σ(1/R_i)).

Why the others don’t fit: the current through each component in parallel isn’t the same—it depends on that branch’s resistance. The total resistance in parallel isn’t the sum of the resistances; it follows the reciprocal rule (the reciprocal of the total equals the sum of reciprocals). And the power dissipated in each branch isn’t necessarily identical; with the same voltage across branches, P_i = V^2 / R_i, so different R_i produce different powers.