Question

An 1875 watt hair dryer 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

Answer 1

The hairdryer is not operating at its fullest capacity when connected to a 110 V source. It uses approximately 1457.5 watts, which is less than its rated power of 1875 watts, and draws about 13.25 amps, below its 15 amp capacity.

Step-by-step explanation:

To determine if the hairdryer is operating at its fullest capacity, we must calculate the actual power being used when it is plugged into a 110 V source and compare that to its rated power of 1875 watts. Using Ohm's Law (V = I * R), where V is voltage, I is current, and R is resistance, we can find the current running through the hairdryer. Since the resistance is given as 8.3 ohms, the current is I = V / R = 110 V / 8.3 Ω ≈ 13.25 A.

Now, to calculate the power (P) being used, we use the formula P = V * I, which gives us P = 110 V * 13.25 A = 1457.5 W. The hairdryer can run at 1875 watts, which is greater than the calculated power usage. Therefore, the hairdryer is not running at its fullest capacity when connected to 110 V.

The question also mentions a capacity of 15 amps, which implies the hairdryer can safely handle up to 15 amps without tripping a standard breaker. As calculated, the hairdryer is using about 13.25 amps, which is below its maximum capacity of 15 amps. So both in terms of wattage and amperage, the hairdryer is not operating at its fullest capacity at 110 V.