Conductor sizing and heating effect: For a given current level in basic electrical wiring, what happens when the wire has a smaller cross-sectional area (thinner conductor)?

Introduction / Context:
When selecting conductors for power or signal wiring, cross-sectional area directly impacts resistance and heating. A thinner wire has higher resistance per unit length, which increases power loss and temperature rise for the same current. This question tests understanding of how geometry affects resistive heating and safety margins in practical circuits.

Given Data / Assumptions:

• The same material (for example, copper) and the same wire length are assumed.
• The current through the conductor is held constant for comparison.
• Steady-state conditions, ignoring skin effect and frequency-dependent phenomena.

Concept / Approach:

Resistance of a uniform conductor is R = rho * L / A, where rho is resistivity, L is length, and A is cross-sectional area. Joule heating in the wire equals P_loss = I^2 * R for a given current I. Therefore, decreasing A increases R and thus increases I^2 * R heating, all else equal.

Step-by-Step Solution:

Verification / Alternative check:

Compare AWG tables: smaller gauge numbers (thicker wires) have lower resistance and lower temperature rise for a given current. Thermal ratings and ampacity charts in wiring standards corroborate that thinner wires must carry lower current to avoid overheating.

Why Other Options Are Wrong:

• Less heat / more conductance / less resistance: opposite of the R versus A relationship.
• No change: contradicts R = rho * L / A and P_loss = I^2 * R.

Common Pitfalls:

• Holding voltage constant instead of current can change current as R changes; however, the core trend that smaller A increases R remains true.
• Ignoring length; doubling length also doubles R, compounding heating.

Final Answer:

more heat