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A resistor with an irregular (non-uniform) cross-section is connected across a constant potential difference source. At the narrower cross-section (point P) and wider cross-section (point Q), which of the following statements is correct?

1. Mean kinetic energy of free electrons at P is greater than at Q.
2. Rate of heat generation per unit length at P is greater than at Q.
3. Rate of electrons crossing per unit area of cross-section at P is less than at Q.
4. Electric field intensity at P is greater than that at Q.

Correct answer: Electric field intensity at P is greater than that at Q.

Solution

The electric field E = rho*J = rho*I/A is inversely proportional to cross-sectional area, so E is largest at P (narrowest). Mean KE of free electrons depends only on temperature (same throughout in steady state), not on drift velocity.

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