Question

Two lightbulbs have powers P1 and P2 when separately connected across an ideal battery with potential difference ΔV. The bulbs are then connected in series across the same battery. Determine the total power consumption of the bulbs in this configuration. (Use any variable or symbol stated above as necessary.)

Answer 1

Answer:

$P'=\dfrac{P_1P_2}{P_1+P_2}$

Explanation:

Lets take

Resistance of bulb 1 =R₁

Resistance of bulb 2 =R₂

As we know that power P

P= ΔV²/R

Given that voltage difference is same for both bulbs

So

P₁R₁= ΔV²       --------1

P₂R₂= ΔV²   -----------2

When these resistance are connected in series then equivalent resistance R

R=R₁+ R₂

The new power P'

P'=ΔV²/R

P'R=ΔV²   ------3

From equation 1 ,2 and 3

P'(R₁+ R₂) = ΔV²

$P'\left(\dfrac{\Delta V^2}{P_1}+\dfrac{\Delta V^2}{P_2}\right)=\Delta V^2$

$P'=\dfrac{P_1P_2}{P_1+P_2}$