A 100-watt lamp glows brighter than a 25-watt lamp. What do you know about the resistances of these two lamps?

Power,P= I^2R

Since power is directly proportional to resistance R, the bulb with greater power will have greater resistance.

P₁₀₀>P₂₅ =>

U²/R₁₀₀ > U²/R₂₅.
Since U = const =>
R₂₅>R₁₀₀

To determine what we know about the resistances of the two lamps based on their wattage, let's start by understanding the relationship between power (measured in watts) and resistance (measured in ohms).

The power dissipated by a device, such as a lamp, can be calculated using the formula: P = V^2 / R, where P is the power in watts, V is the voltage across the device, and R is the resistance of the device.

In this case, we have two lamps: one with a power rating of 100 watts and another with a power rating of 25 watts. We can make a few observations based on this information:

1. Brightness: The 100-watt lamp is brighter than the 25-watt lamp. Since brightness depends on the amount of power a lamp consumes, we can infer that the 100-watt lamp is using more electrical power and emitting more light.

2. Power: The 100-watt lamp has a higher power rating compared to the 25-watt lamp. This means that the 100-watt lamp dissipates more electrical energy per unit of time than the 25-watt lamp.

Now, to directly determine the resistances of the lamps, we need additional information. The wattage rating alone does not provide enough data to calculate the resistance directly. We'd need the voltage or current information to determine the resistance through the formula R = V / I (Ohm's Law) or by knowing the voltage and current ratings of the lamps.

Therefore, based solely on the information given, we can conclude that the 100-watt lamp has a higher resistance than the 25-watt lamp. This is because a higher power rating typically requires a higher resistance to handle the increased power. However, we cannot determine the exact resistance values without more information.