In a parallel circuit, how does current divide and how is total resistance determined?

In a parallel circuit, how does current divide and how is total resistance determined?

• A. Current divides among branches; total resistance is the reciprocal of the sum of the reciprocals.
• B. Current is the same through all branches; total resistance is the sum of the branch resistances.
• C. Current divides among branches; total resistance is the reciprocal of the sum of the reciprocals.
• D. Current through each branch equals its resistance.

Answer: (C)

In parallel, the voltage across every branch is the same, so each branch draws current I_i = V/R_i. The total current is the sum of these branch currents, I_total = V * sum(1/R_i). Because the total current and total voltage relate by V = I_total * R_eq, the equivalent resistance of the parallel network is R_eq = V / I_total = 1 / sum(1/R_i). This is why the total resistance in parallel is the reciprocal of the sum of the reciprocals of the branch resistances. As more parallel paths are added or as branch resistances decrease, the sum of conductances (1/R_i) increases, causing R_eq to drop. For two branches, this gives R_eq = (R1*R2)/(R1+R2).

In parallel, the voltage across every branch is the same, so each branch draws current I_i = V/R_i. The total current is the sum of these branch currents, I_total = V * sum(1/R_i). Because the total current and total voltage relate by V = I_total * R_eq, the equivalent resistance of the parallel network is R_eq = V / I_total = 1 / sum(1/R_i). This is why the total resistance in parallel is the reciprocal of the sum of the reciprocals of the branch resistances. As more parallel paths are added or as branch resistances decrease, the sum of conductances (1/R_i) increases, causing R_eq to drop. For two branches, this gives R_eq = (R1*R2)/(R1+R2).