A 30-W led bulb and a 90-W led bulb are wired in the parallel to a 120-V source. You plug in a third bulb in parallel with the other two and the current increases to a 4.5-A, what is the wattage of the bulb you added? Please explain how you got the answer in steps.
Use the formulas:
Power (watts) = V^2/R
V=voltage in V = 120 V
R=reisistance in Ω
=>
R=V^2/P............(1)
R(30W)=120^2/30=480Ω
R(90W)=120^2/90=160Ω
Now using equation
V=iR
i=current in amps
With three connected in parallel,
i=4.5A
R(equivalent)=V/i=120/4.5=80/3 Ω
Using the parallel resistance formula
R(equivalent)=1/(1/R1+1/R2+1/R3)
or
80/3=1/(1/480+1/160+1/R3)
or
3/80=(1/480+1/160+1/R3)
solve for R3
R3=1/(3/80-1/480-1/160)
=240/7Ω
=34.2857Ω approx.
Now you can substitute R in equation (1) given above to solve for P, the wattage, which turns out to be much greater than the other two.
Post your answer for a check if you wish.
To find the wattage of the added bulb, we need to understand the concept of parallel circuits and how the current flows in them.
In a parallel circuit, the voltage across each branch is the same, while the total current flowing through the circuit is equal to the sum of the currents in each branch.
Let's break down the given information step by step:
1. We have two LED bulbs wired in parallel with a 120-V source, with power ratings of 30 W and 90 W respectively.
2. Since the bulbs are in parallel, the voltage across each of them will be 120 V.
3. We are then adding a third bulb in parallel with the other two.
4. As a result, the total current in the circuit increases to 4.5 A.
Now, using the concept of parallel circuits, we can determine the current flowing through each bulb:
1. For the 30 W bulb, since the voltage across it is 120 V, we can use the formula P = VI (power equals voltage times current) to find the current:
30 W = 120 V × I
I = 30 W / 120 V
I = 0.25 A
2. Similarly, for the 90 W bulb:
90 W = 120 V × I
I = 90 W / 120 V
I = 0.75 A
3. In a parallel circuit, the total current is the sum of the currents in each branch. So, we can add the currents of the two bulbs already connected to find the total current before adding the third bulb:
Total current (before adding third bulb) = 0.25 A + 0.75 A
Total current (before adding third bulb) = 1 A
4. Finally, with the third bulb added, the total current in the circuit becomes 4.5 A. Thus, we can subtract the total current before adding the third bulb from the total current after adding it to find the current through the added bulb:
Current through added bulb = Total current (after adding third bulb) - Total current (before adding third bulb)
Current through added bulb = 4.5 A - 1 A
Current through added bulb = 3.5 A
Now, we can find the wattage of the added bulb:
Power (wattage) of the added bulb = 120 V × 3.5 A
Power (wattage) of the added bulb = 420 W
Therefore, the wattage of the bulb you added is 420 W.