What happens when two lamps rated 40W and 220V each are connected in series? How does the total power dissipation in both lamps change in this configuration?
When two lamps rated 40W and 220V each are connected in series, the voltage across each lamp is halved because the same current flows through both and the total voltage is divided equally between the two. Each lamp receives 110V across it in series, resulting in a new power dissipation for each lamp. The total power dissipation in both lamps will change due to this new configuration.
Explanation of Series Connection for Two Lamps
In a series connection of two lamps rated 40W and 220V each, the voltage is divided between the two lamps. This splitting of voltage results in each lamp receiving half of the total voltage, which is 110V individually. The key aspect of series connection is that the same current flows through both lamps.
Calculating the New Power Dissipation:
To calculate the new power dissipated by each lamp in the series connection, we can use the formula P = V^2 / R, where P is the power, V is the voltage, and R is the resistance.
First, let's find the resistance of one lamp using the original power rating and voltage:
R = V^2 / P = (220)^2 / 40 = 1210 ohms
Next, we can calculate the new power at 110V for each lamp:
P = V^2 / R = (110)^2 / 1210 = 10W
Therefore, when the two lamps are connected in series at 110V each, the power dissipated by each lamp is 10W. The total power dissipated in both lamps will be 10W + 10W = 20W. This shows that the total power dissipation changes when two lamps rated 40W and 220V each are connected in series.