Two 200 W (120 V) lightbulbs are wired in series, then the combination is connected to a 120 V supply. How much power is dissipated by each bulb?
All calculations are done with the assumption that the resistance of the light bulbs remain constant.
P = E^2/R.
200 = 120^2/R,
R = 72 Ohms.
P = 60^2/72 = 50 Watts = Power dissipated by each bulb.
To find out how much power is dissipated by each bulb, we need to first determine the total power dissipated by the combination of the two bulbs wired in series.
When light bulbs are connected in series, the total resistance is equal to the sum of each bulb's resistance. Therefore, we need to find the resistance of each bulb.
We can use Ohm's Law to calculate the resistance of each bulb:
Resistance (R) = Voltage (V) / Current (I)
Since we know the power (P) and voltage (V) for each bulb, we can use the formula P = IV to calculate the current (I) for each bulb.
For the first bulb:
Power (P1) = 200 W
Voltage (V1) = 120 V
Current (I1) = P1 / V1
For the second bulb:
Power (P2) = 200 W
Voltage (V2) = 120 V
Current (I2) = P2 / V2
Once we have the current (I) for each bulb, we can calculate the resistance (R) using Ohm's Law.
For the first bulb:
Resistance (R1) = V1 / I1
For the second bulb:
Resistance (R2) = V2 / I2
Finally, the total resistance (RTotal) of the combination can be calculated by adding the resistances (R1 + R2).
Now, we can calculate the power dissipated by each bulb.
For the first bulb:
Power dissipated by bulb 1 = I1^2 * R1
For the second bulb:
Power dissipated by bulb 2 = I2^2 * R2
To find out how much power is dissipated by each bulb, we need to understand how power behaves in a series circuit.
In a series circuit, the same current flows through all the components. This means that in our case, the same current will flow through both lightbulbs.
We can use Ohm's Law to calculate the current flowing in the circuit:
Current (I) = Voltage (V) / Resistance (R)
Since the bulbs are identical, they have the same resistance. To find the resistance of each bulb, we can rearrange Ohm's Law:
Resistance (R) = Voltage (V) / Current (I)
Let's calculate the resistance:
Resistance (R) = 120 V / Current (I)
Now, we know that power (P) is calculated using the equation:
Power (P) = Voltage (V) * Current (I)
Since the voltage across each bulb is the same (120 V), and the current passing through each bulb is the same in a series circuit, the power dissipated by each bulb is equal.
So, to find the power dissipated by each bulb, we need to calculate the current flowing through the series circuit, and then use that current to calculate the power.
1. Calculate the current (I):
Using Ohm's Law, we can calculate the total resistance of the series circuit:
Total Resistance (R_total) = Resistance of one bulb + Resistance of the other bulb
Since the bulbs are identical, the resistance of each bulb is the same, and we can calculate the total resistance by:
Total Resistance (R_total) = 2 * Resistance of one bulb
Now, using Ohm's Law, we can calculate the current:
Current (I) = Voltage (V) / Total Resistance (R_total)
2. Calculate the power (P) dissipated by each bulb:
Power (P) = Voltage (V) * Current (I)
Now you can substitute the values and calculate the power dissipated by each bulb.