Q145
General SciencePhysics
If the length of the filament of a heater is reduced by 10%, the power of the heater will
- a.increase by about 9%
- b.increase by about 11%
- c.increase by about 19%
- d.decrease by about 10%
Answer: (B) increase by about 11%
For a heater on a fixed supply voltage, $P=\frac{V^2}{R}$ and $R=\rho\frac{L}{A}\propto L$. Reducing the length by 10% makes $R'=0.9R$, so $P'=\frac{V^2}{0.9R}\approx1.11P$ - an increase of about 11%. Option (D) wrongly assumes power falls with length, and the 19% figure comes from wrongly using $1-0.9^2$. Moral: a shorter (or thicker) filament has lower resistance, draws more current and gives more heat at the same voltage.