Circuit question (physics)

Question

Two filament lamps a1 and a2 of nominal capacity a1=40W and a2=60W are designated for same voltage U0, connected into series electric circuit with voltage of U0. What is the power each lamp will use? Which one will shine brighter?

Answer 1

Two filament lamps a1 and a2 of nominal capacity a1=40W and a2=60W are designated for same voltage U0, connected into series electric circuit with voltage of U0. What is the power each lamp will use? Which one will shine brighter?

Hello Armad,

Here is the solution :

Power = Voltage²/Resistance = V² /R Also Power = Current ² *Resistance

Power 1 = U0²/R₁ = 40, so R₁ = U0²/40

Power 2 = U0²/ R₂ =60, so R₂ =U0²/60

Thus R₁ is greater than R₂

Now the two connected in series to the same voltage U₀

Total Resistance = R₁ +R₂

Current through each = U0/( R₁ +R₂ )

New Power Of a1 =Current ²*R₁ =U0² R_1/ (R₁ +R₂)²

New power of a2 = Current²*R₂ = U0² R₂/ (R₁ +R₂)²

Now plug in the values of R₁ and R_2, From above expressions

and compare two new powers of a1 and a2