A clothes dryer will draw _ amps when operated at 208 volts. The dryer nameplate states that it is rated for 9.7 kW at 240 volts. Select one: a. 53.81 b. 5.94 c. 35.03 d. 40.42 e. 9.7
The correct answer and explanation is:
Correct Answer: c. 35.03
Step-by-Step Explanation:
To calculate the current (amps) a dryer draws at 208 volts when its nameplate shows 9.7 kW at 240 volts, we must first understand the relationship between power, voltage, and current using the formula: Power (P)=Voltage (V)×Current (I)\text{Power (P)} = \text{Voltage (V)} \times \text{Current (I)} I=PVI = \frac{P}{V}
However, the power rating of 9.7 kW is given at 240 volts, not at 208 volts. Since the voltage is lower than what the appliance is rated for, the actual power output (watts) decreases proportionally.
Step 1: Adjust the power to 208 volts
Because most electric dryers use resistive heating elements, and resistance stays constant, the power used at 208 volts can be estimated using this formula: P208=P240×(208240)2P_{208} = P_{240} \times \left(\frac{208}{240}\right)^2 P208=9700×(208240)2P_{208} = 9700 \times \left(\frac{208}{240}\right)^2 P208=9700×(0.8667)2=9700×0.7511=7286watts(approx.)P_{208} = 9700 \times \left(0.8667\right)^2 = 9700 \times 0.7511 = 7286 watts (approx.)
Step 2: Find the current at 208 volts
Now use the basic formula: I=PV=7286208≈35.03 ampsI = \frac{P}{V} = \frac{7286}{208} \approx 35.03 \text{ amps}
Summary
Although the dryer is rated for 9.7 kW at 240V, when supplied with 208V (a common commercial voltage), the power drops to about 7286 watts due to the fixed resistance of the heating element. Using Ohm’s Law, this power draw results in a current of about 35.03 amps.
Thus, the correct answer is:
c. 35.03