Final answer:
The peak current through the 500-W room heater operating on 120-V AC power is 4.17 A.
Step-by-step explanation:
To calculate the peak current through a 500-W room heater operating on 120-V AC power, we can use the formula:
 
Peak Current (Ipeak) = Power (P) / Voltage (V)
 
Substituting the given values, we get:
 
Ipeak = 500 W / 120 V
 
Simplifying the equation:
 
Ipeak = 4.17 A
 
Therefore, the peak current through the room heater is 4.17 A (option a).