Question

A car’s headlights dissipate 40 W on low beam and 50 W on high beam. Is there more or less resistance in the high-beam filament?

Answer 1

The high-beam filament of a car’s headlights has less resistance than the low-beam filament, as it dissipates more power and draws more current when the voltage is constant.

Step-by-step explanation:

The student is asking whether there is more or less resistance in the high-beam filament of a car’s headlights compared to the low beam, given that high beam uses 50 W and low beam uses 40 W. Assuming that the voltage supplied to both filaments is the same, the filament with the higher power dissipation (high beam) would draw more current.

According to Ohm's law, which describes the relationship between voltage (V), current (I), and resistance (R) as V = IR, if the voltage is constant, a higher current would mean lower resistance. Therefore, the high-beam filament has less resistance compared to the low-beam filament, which is consistent with the discussion that resistance increases with temperature and the bulb draws more current when the resistance is lower.

Answer 2

The high-beam filament has more resistance than low beam filament.

Step-by-step explanation:

To determine if the 50 W dissipated by a car’s headlights on high beam, has more or less resistance, formula for power dissipated in the filament is used.

Power = IV

Voltage =IR

∴ Power = I*IR = I²R

where;

I is the current

V is the voltage

R is the resistance

From the equation above, Power dissipated is directly proportional to Resistance.

Hence, the high-beam filament has more resistance than low beam filament.