What will be the total power of a 40W and a 60W bulb when connected in series with the same source?
When connected in series across the same source, the total power of the 40W and 60W bulbs will be 24W.
Explanation:
When bulbs are connected in parallel, they receive the same voltage from the source, and the total power is the sum of the individual powers. In this case, a 40W and a 60W bulb connected in parallel result in a total power of 100W.
However, when bulbs are connected in series, the total resistance in the circuit increases, reducing the overall power consumption. To calculate the total power in a series circuit, we need to use the formula:
\[P_{\text{total}} = \frac{V^2}{R_{\text{total}}}\]
Where \(P_{\text{total}}\) is the total power, \(V\) is the voltage, and \(R_{\text{total}}\) is the total resistance.
Since both bulbs have different wattages, their resistances (R1 and R2) will be different as well. Using the formula \(P = \frac{V^2}{R}\), we can calculate their individual resistances:
For the 40W bulb:
\[R_1 = \frac{V^2}{40W}\]
For the 60W bulb:
\[R_2 = \frac{V^2}{60W}\]
The total resistance in a series circuit is the sum of individual resistances:
\[R_{\text{total}} = R_1 + R_2 = \frac{V^2}{40W} + \frac{V^2}{60W}\]
Now, to find the total power when connected in series, we can use the formula:
\[P_{\text{total}} = \frac{V^2}{R_{\text{total}}}\]
However, since the voltage remains the same as when the bulbs were in parallel, the total power will be:
\[P_{\text{total}} = 24W\]
So, when connected in series with the same source, the total power of the 40W and 60W bulbs will be 24W.