# Two 60W-lightbulbs are connected on 220 V AC-voltage - how much electric power is spent by each lightbulb? [closed]

Two 60W-lightbulbs are connected on 220 V AC-voltage - how much electric power is spent by each lightbulb?

There are two scenarios:

In one, these two lighbulbs are connected serially, and in the other parallelly. The trouble is, no resistance value is given, so I don't know how electric power can be calculated for each bulb. No amperage given either.

How do I proceed?

Edit: Thanks to the answer I did figure out the power consumption for each connection.

Serially:

$P=\dfrac{U^2}{R} => R=\dfrac{U^2}{P}$

At 220 Volt and 60 W the resistance is $806 \dfrac{2}{3}$ ohm for each bulb. In a serial connection the resistances add up, meaning, the two bulbs together have $1613 \dfrac{1}{3}$ ohm. Repeating the above formula, we get a total power consumption of $30$ watt. So each bulb consumes $15$ watt.

Parallelly:

The total resistance in a parallel connection can be calculated as

$R_T=\dfrac{R_1*R_2}{R_1+R_2}$

which is $403 \dfrac{1}{3}$ ohm. Thus, again repeating the formula for power consumption $\big(P=\dfrac{U^2}{R}\big)$, the total power consumption is $120$ watt. Which is $60$ watt for each bulb.

• I'm going to take a complete guess and say that each is consuming 60W of power. – Ignacio Vazquez-Abrams Jun 16 '12 at 16:47
• When ordered parallelly, they do, as I found out. I guess, lightbulbs are nowadays manufactured with parallel connections in mind. – Miroslav Cetojevic Jun 17 '12 at 9:47

Use this formula:
Watt = (Voltage x Voltage)/Resistance
and hence the restistace of the bulb would be (220x220)/60 = 806.67 ohm

Hope it helps and you can proceed now very easily.

• Yes, it helped. Can't believe I forgot this formula. Thanks. – Miroslav Cetojevic Jun 17 '12 at 9:46

Assuming the light bulbs are rated for 60W @ 220V then, when connected in parallel, each dissipates 60W since there is 220V across each bulb.

When connected in series, assuming the light bulbs are identical, there is just 110V across each bulb.

If a light bulb were equivalent to a linear resistor then each light bulb would dissipate 15W since power is proportional to the square of the voltage; when the voltage is reduced by a factor of 2, the power is reduced by a factor of 4.

However, I believe a light bulb is a non-linear resistance. Thus, unless the resistance versus voltage curve is known for the bulb, you cannot calculate the power for each bulb when connected in series. One way to proceed is to connect an ammeter in series with the two series connected bulbs.

• For the sake of argument, the lighbulbs have linear resistances. Nonetheless, thanks for your answer. – Miroslav Cetojevic Jun 17 '12 at 9:45

power cosumed in KWH by 1 bulb=60*1/1000=.06 unit in one hour if the two bulbs are in parallel connected