1. Outlets of two rooms are placed in parallel on a single circuit (120 volts). How many 100 watt light bulbs could you run on a circuit that had a 15 amp circuit breaker (max of 15 amps total)
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Each 100 W lamp draws I = P/V = 100/120 = 0.83 Amps, if 120 volts is applied to it. The number of lamps it takes to use a total of 15 Amps is therefore ___
Don't be confused by the number of rooms. And don't assume the lamps are in series. They are all in parallel from a power line with a single circuit breaker.
To solve this problem, we need to consider the current (in amps) drawn by each 100 watt light bulb.
Given:
- Voltage (V) = 120 volts
- Power (P) of each light bulb = 100 watts
Step 1: Calculate the current drawn by each light bulb.
We can use the formula I = P/V, where I is the current in amps, P is the power in watts, and V is the voltage.
For each light bulb:
I = 100/120 = 0.83 amps
Step 2: Calculate the total current drawn by all the light bulbs.
Since the outlets are in parallel, the total current drawn is the sum of the currents drawn by each light bulb.
Let's assume the number of light bulbs is "x."
Total Current = x * 0.83 amps
Step 3: Determine the maximum number of light bulbs that can be powered by the 15 amp circuit breaker.
The circuit breaker has a maximum limit of 15 amps. Therefore, we need to calculate the maximum value of "x" that satisfies the equation:
x * 0.83 amps ≤ 15 amps
Solving for "x":
x ≤ 15 amps / 0.83 amps
x ≤ 18.072
Since "x" represents the number of light bulbs, it must be a whole number. Therefore, the maximum number of 100 watt light bulbs that can be run on the circuit is 18.
Note: In practice, it's recommended to leave some margin for safety, so it would be wise to not exceed 80% of the circuit breaker's maximum capacity. In this case, it would be best to limit the number of light bulbs to 14 or 15.