If three resistors of 3 ohms, 5 ohms, and 22 ohms are connected in series in a 28-volt circuit, how much current will flow through the 3-ohm resistor?

Question

BlackTom AI · Accepted Answer

1. Relevant knowledge points and concepts
In a series circuit the same current flows through all components because there is a single path for charge. Ohm’s law (V = I·R) relates voltage (V), current (I), and resistance (R). Total resistance in series equals the sum of individual resistances: R_total = R1 + R2 + R3.

2. Complete reasoning process step by step
- Identify resistances: R1 = 3 Ω, R2 = 5 Ω, R3 = 22 Ω.
- Total resistance in series: R_total = 3 + 5 + 22.

3. Calculations with intermediate steps
- R_total = 3 + 5 + 22 = 30 ohms.
- Use Ohm’s law to find current: I = V / R_total.
- I = 28 V / 30 Ω = 28/30 A = 0.933333... A.
- Rounding to two decimal places gives I ≈ 0.93 A.

As a consistency check, calculate individual voltage drops: V3Ω = I·3 = 0.933333...×3 = 2.8 V; V5Ω = 0.933333...×5 = 4.666666... V; V22Ω = 0.933333...×22 = 20.533333... V. Sum = 2.8 + 4.666666... + 20.533333... = 28 V, matching the supply.

4. Why the correct answer is correct
Because the resistors are in series the current is equal through each resistor and is determined by the total series resistance. Using V = I·R_total yields 28/30 = 0.9333... A, which when rounded to two significant figures is 0.93 ampere.

5. Why the other options are incorrect
- 9.3 amperes: This treats only the 3 Ω resistor as the total resistance (28/3 ≈ 9.33 A), ignoring the other resistors in series—incorrect.
- 1.05 amperes: This value does not result from the correct total resistance (30 Ω) and so does not satisfy Ohm’s law for this series combination.

6. Conclusion
The current through the 3-ohm resistor is 0.93 ampere. This matches the provided correct answer: 0.93 ampere.

If three resistors of 3 ohms, 5 ohms, and 22 ohms are connected in series in a 28-volt circuit, how much current will flow through the 3-ohm resistor?单项选择题

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