Question

two electric bulbs of the same power, but with different marked voltages are connected in series across a power line . Then their brightness will be​

Answer 1

Answer:

Rating of bulbs hasn't been specified which is very important. Let's assume each bulb is rated at 120V,50Hz supply. Now what it means is that when 40W (or 60W) bulb will be connected across rated voltage i.e.120V ac supply then power dissipation across it will be 40W (or 60W). Rating is important because say if 40W bulb rated at 120V supply is connected across 220V supply then it will not work (might burn or blow up), meaning thereby a device can not work at a voltage much higher than its rated voltage.

One more information that you get from rating is the resistance of each bulb.

P=(V*V)/R

Since both bulbs are rated at same voltage, we can say that resistance of each bulb is inversely proportional to its rated power. Therefore

R (40W bulb) > R (60W bulb)

We should know that the bulb across which power dissipation is more will glow brighter. Now

1. When connected in series: In a series connection, current flowing across each element is same. So when 40W bulb and 60W bulb are connected in series, same current will flow through them. To find which bulb will glow brighter we need to find the power dissipation across each of them. From the relation

P=(I*I) R

since current is same we can say that power dissipation will be higher for the bulb with higher resistance i.e. 40W bulb.

Hence 40W bulb will glow brighter in series connection.

2. When connected in parallel: In a parallel connection, voltage across each element is same. So when 40W bulb and 60W bulb are connected in parallel, voltage across them will be same (100 V in the given case). To find which bulb will glow brighter we need to find the power dissipation across each of them. From the relation

P=(V*V)/R

since voltage is same we can say that power dissipation will be higher for the bulb with lower resistance i.e. 60W bulb.

Hence 60W bulb will glow brighter in parallel connection

Answer 2

Given that,

Two electric bulbs of the same power, but with different marked voltages are connected in series across a power line.

To find,

Their brightness will be?

Solution,

The marked power is given by :

$P=\dfrac{V^2}{R}$

R is resistance and V is marked voltage

$R=\dfrac{V^2}{P}$

As power of both bulbs is same and voltages are different. Both bulbs are connected in series, so current in both of them will be same. It means that the brightness is same as $R\propto V^2$.