Question

Which bulb will glow brighter, a 40 Watt bulb or a 60 watt when connected in series. Why?

Answer 1

For sake of simplicity, let's assume that the bulbs are rated at 100V and more power a bulb consumes the brighter it is.
The bulbs are in series so the amount of current flowing through each is same. The two resistances (assuming pure resistance) are in series. So
$R_1=\frac{{100}^2}{60}$ for 60 Watt bulb
$R_2=\frac{{100}^2}{40}$ for 40 Watt bulb
Current drawn $I=\frac{V}{(R1+R2)}=\frac{100}{\left[{100}^2\right(\frac{1}{60}+\frac{1}{40}\left)\right]}=60\times \frac{40}{100}\times (60+40)$
Power Consumer by bulb1= $I^{2}R1={60}^2\times \frac{{40}^2}{{100}^2}\times (60+40{)}^2\times \frac{{100}^2}{60}$
$={\frac{60\times {40}^2}{(60+40)}}^2=9.6$ Watts
Power Consumer by bulb2= $I^{2}R2=40\times \frac{{60}^2}{(60+40{)}^2}=14.4$ Watts (this is similar to the expression above)
So 40 Watts bulb glow brighter. The trick is that a bulb is essentially just a resistance so $\frac{40W}{60W}$ can only consume that kind of power when it is available.Like inn my assumption when connected in parallel to the AC source (100 V). Current may change voltage may change wattage may change resistance will remain invariant, ermm for the scope of this discussion alone. Find the quantity that is invariant and jobs done.