Three identical resistors are connected in series to a battery. If a current of 12 A flows from the battery, how much current flows through any one of the resistors?

Question

BlackTom AI · Accepted Answer

In a series circuit the current is the same through every component, so the current through each resistor equals the battery current.

1. Relevant knowledge points and concepts
- Series connection: components are arranged end-to-end with no branching nodes between them.
- Kirchhoff’s current law (conservation of charge): at any node the sum of currents entering equals the sum leaving; a series chain has no node where current can split.
- Therefore the same current flows through each element in a series circuit regardless of their individual resistances (provided the circuit is closed).

2. Step-by-step reasoning
- The battery supplies a single current of 12 A into the series chain.
- Because the three resistors are connected one after another with no branches, charge that flows into the first resistor must flow into the second and then into the third. There is nowhere for the current to divide or change value.

3. Calculations (intermediate steps shown)
- Let I be the current from the battery: I = 12 A.
- Currents through resistors: I1 = I, I2 = I, I3 = I.
- Thus I1 = I2 = I3 = 12 A.
(If one wanted to relate to voltage and resistance: total R = 3R; I = V/(3R) = 12 A → V = 12·3R = 36R; voltage across each resistor = I·R = 12R. These do not change the fact the current is 12 A through each resistor.)

4. Why the correct answer is correct
- The defining feature of series circuits is a single common current. Since the battery current is given as 12 A, each resistor must carry that same 12 A.

5. Why the other options are incorrect
- 4 A would be correct only if the total current 12 A were somehow split equally among three parallel branches; that is not the case in a series connection.
- 36 A would imply the current increased through components, which contradicts conservation of charge—current cannot increase in a series string.
- Zero would be true only if the circuit were open or broken; the problem states 12 A flows, so it is not open.

6. Conclusion
Therefore the current through any one of the resistors is 12 A, matching the provided correct answer: 12 A.

Three identical resistors are connected in series to a battery. If a current of 12 A flows from the battery, how much current flows through any one of the resistors?单项选择题

类似问题

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

In the circuit below, vs = -2 Volts, R1 = 9Ω, R2 = 6Ω. Find i in Amps. Give your answer to 3 decimal places.

In the circuit below, vs = 2 Volts, R1 = 8Ω, R2 = 7Ω. Find i in Amps. Give your answer to 3 decimal places.

A 12 V potential difference is applied across a series combination of four 6 Ω resistors. The current in each resistor is

A circuit has an applied voltage of 24 volts and a load consisting of a 10-ohm resistor in series with a 30-ohm resistor. What is the voltage drop across the 10-ohm resistor?

How many loops are there in this circuit? Express your answer as an integer.

If I make a simple circuit with a 5 volt battery and a single light bulb then I can expect the voltage across the lightbulb to be 5 volts. If I add another five volt battery to the circuit I can expect the voltage across the bulb to be_. I can also expect the current through the bulb to__.

I have a simple circuit running off a battery powering a lightbulb (bulb A). If I add another light (bulb B) in series with bulb A I can expect that the voltage across bulb A will _ and bulb A will shine___.

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单