Lamps with the same value of resistance can have different wattage ratings if the ? ratings are different
a. current b. impedance c. resistance d. voltage
The correct answer and explanation is:
The correct answer is d. voltage.
Explanation:
The wattage rating of a lamp (or any electrical device) is determined by the power it consumes, which is directly related to the voltage applied to it and the current flowing through it. This relationship is described by the formula for electrical power: P=V×IP = V \times I
Where:
- P is the power in watts (wattage),
- V is the voltage in volts,
- I is the current in amperes.
If two lamps have the same resistance, their wattage rating will be different if the applied voltage is different. According to Ohm’s Law, the relationship between voltage, current, and resistance is: V=I×RV = I \times R
Where:
- R is the resistance in ohms.
Rearranging this equation for current, we get: I=VRI = \frac{V}{R}
Substituting this into the power equation gives: P=V×VR=V2RP = V \times \frac{V}{R} = \frac{V^2}{R}
From this equation, it is clear that the power (wattage) is proportional to the square of the voltage. If the resistance is fixed, a higher voltage applied to the lamp will result in a higher power consumption (wattage). Conversely, if the voltage is lower, the wattage will also be lower, even if the resistance is the same.
For example, a lamp with a resistance of 10 ohms connected to a 12-volt power supply will consume more power than the same lamp connected to a 6-volt supply because the power is proportional to the square of the voltage. Therefore, lamps with the same resistance can have different wattage ratings based on the voltage supplied to them.