Question

An 1875-watt hairdryer has a resistance of 8.3 ohms and a capacity of 15 amps if 110 V of electricity is delivered to the hairdryer, then is the hairdryer operating at its fullest capacity? Explain your answer and support your answer with mathematical evidence.

a) Yes, as Power = Voltage x Current and is within the limit.
b) No, as the resistance is too high for the specified voltage.
c) Yes, as the product of voltage and current is within the power limit.
d) No, as the product of voltage and current exceeds the power limit.

Answer 1

The 1875-watt hairdryer with a resistance of 8.3 ohms is not operating at its full capacity when 110 volts and 15 amps are delivered because the resulting power is only 1650 watts, which is less than its rated power.

Step-by-step explanation:

To determine if the 1875-watt hairdryer is operating at its fullest capacity with a resistance of 8.3 ohms and a capacity of 15 amps when 110 V of electricity is delivered, we need to calculate the actual power used by the hairdryer using the power formula and compare it to its rated power.

The power can be calculated using the formula: Power (P) = Voltage (V) x Current (I). Given that the hairdryer has a capacity of 15 amps, if it were operating at full capacity at 110 volts, the power would be:

P = 110 V x 15 A = 1650 watts

This is less than the hairdryer's rated power of 1875 watts. Therefore, even at 15 amps, the hairdryer is not operating at its fullest capacity when 110 V of electricity is delivered to it.

The correct answer is: c) Yes, as the product of voltage and current is within the power limit.