Which one of the following statements is true about a series circuit?

Question

BlackTom AI · Accepted Answer

In a series circuit the current is the same through every component and the source voltage is shared (divided) among the components; this follows from conservation of charge and energy (Kirchhoff’s laws).

Relevant concepts:
- Conservation of charge: with a single path (series), the same number of charges per second flow through each element, so the current I is identical at all points.
- Kirchhoff’s Voltage Law (KVL): the algebraic sum of voltage changes around a closed loop equals zero, so the battery voltage equals the sum of the voltage drops across each series element: Vbattery = V1 + V2 + ... + Vn.
- Ohm’s law: V = I·R relates current, voltage and resistance for each element.

Step-by-step reasoning with a numerical example:
1. Suppose a 12 V battery supplies two resistors in series: R1 = 2 Ω and R2 = 4 Ω.
2. Total resistance Rtotal = R1 + R2 = 2 + 4 = 6 Ω.
3. Current in the loop: I = Vbattery / Rtotal = 12 V / 6 Ω = 2 A. This same 2 A flows through both resistors (no alternate paths).
4. Voltage across R1: V1 = I·R1 = 2 A · 2 Ω = 4 V. Voltage across R2: V2 = I·R2 = 2 A · 4 Ω = 8 V.
5. Check sum: V1 + V2 = 4 V + 8 V = 12 V = Vbattery, confirming voltages add to the battery voltage.

Why option b is correct:
- It states exactly the two key properties above: current remains the same in series, and voltages across components add to the battery voltage.

Why the other options are incorrect:
- a. “Current increases as it goes around… voltage decreases to zero.” Incorrect — current does not increase; it is constant. Voltage drops sum to the source but do not cause current to increase.
- c. “Currents add up… voltage remains the same.” That describes a parallel circuit, not series.
- d. “The current gets less as it goes around.” Incorrect — with one path the current is uniform; it does not diminish around the loop.

Conclusion: The correct answer is b. The current remains the same and the voltages across each component add up to the battery voltage.

Which one of the following statements is true about a series circuit?单项选择题

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