Two circuits (the figure below) are constructed using identical, ideal batteries (emf = E ) and identical lightbulbs (resistance = R). If each bulb in circuit 1 dissipates 4.00 W of power, how much power does each bulb in circuit 2 dissipate? Ignore changes in the resistance of the bulbs due to temperature changes.
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To find the power dissipated by each bulb in circuit 2, we can use the formula:
Power = (Voltage)^2 / Resistance
In this case, both circuits use identical batteries with the same EMF (electromotive force) and identical lightbulbs with the same resistance. Therefore, the voltage across each bulb in both circuits is the same.
In circuit 1, the power dissipated by each bulb is given as 4.00 W. This means we can find the voltage across each bulb in circuit 1.
Let's denote the voltage across each bulb in circuit 1 as V1.
Power = V1^2 / R
Given: Power = 4.00 W and R = Resistance
Now, we can use this formula to find the voltage across each bulb in circuit 1:
V1^2 = Power * R
V1 = sqrt(Power * R) (Taking the square root of both sides)
Now, we know the voltage across each bulb in circuit 1. Let's denote the voltage across each bulb in circuit 2 as V2.
Since both circuits use identical batteries, the voltage across each bulb in circuit 2, V2, is also V1.
Finally, we can find the power dissipated by each bulb in circuit 2 using the formula:
Power = V2^2 / R = V1^2 / R = 4.00 W
Therefore, each bulb in circuit 2 dissipates 4.00 W of power.