In a series circuit, which statement is true?

In a series circuit, which statement is true?

• A. Currents add and voltages are equal.
• B. Voltages add and currents are equal.
• C. Currents are equal; resistances add (R_eq = R1 + R2).
• D. Both currents and voltages sum to zero.

Answer: (C)

In a series circuit, there is only one path for current, so the same current flows through every component. Because the same current passes through each resistor, the total or equivalent resistance adds up: R_eq = R1 + R2. That means the source voltage V_total equals I times that total resistance, and the voltage across each resistor is V_i = I × R_i. So the defining truth is that currents are equal through all elements and the resistances simply add to give the total resistance. The other statements aren’t as precise descriptions of series behavior. Currents do not add in a single path; they remain the same through each element. While voltages across components do add up to the source voltage, stating that only voltages add while keeping currents equal is less complete than the direct relationship that ties the same current to a sum of resistances.

In a series circuit, there is only one path for current, so the same current flows through every component. Because the same current passes through each resistor, the total or equivalent resistance adds up: R_eq = R1 + R2. That means the source voltage V_total equals I times that total resistance, and the voltage across each resistor is V_i = I × R_i. So the defining truth is that currents are equal through all elements and the resistances simply add to give the total resistance.

The other statements aren’t as precise descriptions of series behavior. Currents do not add in a single path; they remain the same through each element. While voltages across components do add up to the source voltage, stating that only voltages add while keeping currents equal is less complete than the direct relationship that ties the same current to a sum of resistances.