Two 95.0 W (120 \rm V) lightbulbs are wired in series, then the combination is connected to a 120 V supply How much power is dissipated by each bulb?
Figure the resistance of each bulb.
Power= V^2/R
R= 120^2/95
Now that two are in series
power total= V^2/2R= 95/2
power each= 95/4 watts.
Please type your subject in the School Subject box. Any other words, including obscure abbreviations, are likely to delay responses from a teacher who knows that subject well.
To find out the power dissipated by each bulb, we can apply the principles of series circuits.
1. Recall that in a series circuit, the current passing through each component is the same.
2. The total voltage in a series circuit is equal to the sum of the voltages across each component.
In this case, two lightbulbs with a power rating of 95.0 W and a voltage rating of 120 V are connected in series to a 120 V supply.
Since the lightbulbs are connected in series, the current passing through each bulb is the same. We can represent this current as "I".
Using Ohm's Law (V = I * R) and the formula for power (P = V * I), we can rearrange the equations to solve for the unknowns.
Let's denote the resistance of each lightbulb as "R". Since power equals voltage multiplied by current (P = V * I), we can write:
P1 = V1 * I ... (1) (for the first bulb)
P2 = V2 * I ... (2) (for the second bulb)
Since each bulb has the same voltage rating, V1 = V2 = V. And from the problem statement, V = 120 V. Substituting this value:
P1 = 120 V * I ... (3)
P2 = 120 V * I ... (4)
Now, we know that the power dissipated by each bulb is 95.0 W. Therefore, we can set up the following equations:
P1 = 95.0 W ... (5)
P2 = 95.0 W ... (6)
Substituting the equations (3), (4), (5), and (6), we get:
120 V * I = 95.0 W ... (7)
120 V * I = 95.0 W ... (8)
Since the equations (7) and (8) are identical, it means that the power dissipated by each bulb is the same, which is 95.0 W.
Therefore, each lightbulb will dissipate 95.0 W of power when connected in series to a 120 V supply.