The figure shows conventional current passing through a resistor. The arrow shows the direction in which this conventional current is flowing. Which of the following statements are correct? (There could be more than one correct choice.)

Question

BlackTom AI · Accepted Answer

Conventional current flows from higher to lower electric potential, and in a steady series circuit the same current flows through every cross section of the wire.

1) Relevant knowledge points and concepts
- Ohm’s law: the voltage drop across a resistor is V = I·R. For a resistor with current I flowing from point a to point b, the potential difference Va - Vb = I·R > 0, so Va > Vb.
- Conservation of charge / Kirchhoff’s current law: in a single series path (no branches), the current is the same at every point along the conductor in steady state.
- Drift speed relation: current I = n·q·Av_d (where n is carrier density, q charge, A cross-sectional area, v_d drift speed). If n and A are unchanged, constant I implies constant v_d; however, without explicit geometry or material changes one cannot infer a change in speed.

2) Step-by-step reasoning
- The arrow shows conventional current from a toward b. Apply Ohm’s law to the resistor R: Va - Vb = I·R. Because R>0 and I>0, Va - Vb is positive, so Va > Vb. Therefore the electric potential is lower at b than at a.
- For the current: since the wire and resistor form a single series path, charge that passes point a per second must also pass point b per second; thus I(a) = I(b).

3) Calculations / intermediate steps
- Va - Vb = I·R (symbolic calculation showing a positive drop from a to b).
- I(a) = I(b) by conservation of charge in steady state (no accumulation of charge in the segment).

4) Why the correct answers are correct
- "The electric potential is lower at point b than at point a." Follows directly from Va - Vb = I·R > 0.
- "The current at point b is the same as the current at point a." Follows from steady-state current conservation in a single series conductor.

5) Why other options are incorrect
- "Charges are moving slower at point b than at a." Not necessarily true; with uniform wire and material, v_d is the same because I is the same. The statement claims a speed change without justification, so it is incorrect.
- "The electric potential is higher at point b than at point a." Opposite of the correct sign; incorrect.
- "The electric potential at point b is the same as it is at point a." Incorrect because there is a voltage drop across the resistor (unless R = 0, which is not stated).

Conclusion: The correct choices are (1) the electric potential is lower at point b than at point a, and (2) the current at point b is the same as the current at point a — matching the provided answers.

The figure shows conventional current passing through a resistor. The arrow shows the direction in which this conventional current is flowing. Which of the following statements are correct? (There could be more than one correct choice.)多项选择题

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