The potential difference across a conductor of resistivity e is constant. The…
2016
The potential difference across a conductor of resistivity e is constant. The heat generated in the conductor is directly proportional to
- A.
e
- B.
1/√e
- C.
1/e
- D.
e2
Attempted by 8 students.
Show answer & explanation
Correct answer: C
Joule's law of heating gives the heat produced in a resistor as H = I2 R t for a fixed current I, or as H = (V2 / R) t for a fixed potential difference V across it. Resistance itself follows R = e L / A, where e is the resistivity and L, A are the conductor's length and cross-sectional area, so R ∝ e.
The problem keeps the potential difference V across the conductor constant, so the applicable relation is H = (V2 / R) t.
Since the conductor's length L and cross-sectional area A do not change, R = e L / A shows that R ∝ e.
Substituting R ∝ e into H = (V2 / R) t, and noting that V and t are both constant, gives H ∝ 1/R ∝ 1/e.
As a check, doubling e doubles R since R ∝ e; with V and t unchanged, H = (V2 / R) t then becomes half. This inverse behaviour matches H ∝ 1/e, confirming the result.