Circuit question (physics)?
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?
Sorry for my english
- micatkieLv 71 month agoFavorite Answer
Resistance of a₁, R₁ = Uₒ²/P₁ = Uₒ²/40 Ω
Resistance of a₂, R₂ = Uₒ²/P₂ = Uₒ²/60 Ω
Equivalent resistance of the two lamps, R = (Uₒ²/40) + (Uₒ²/60) = 0.416Uₒ²
Current of the series current, I = Uₒ/R = Uₒ/(0.416Uₒ²) = 24/Uₒ A
In the series circuit:
Power of a₁ = I²R₁ = (24/Uₒ)² × (Uₒ/40) = 14.4 W
Power of a₂ = I²R₂ = (24/Uₒ)² × (Uₒ²/60) = 9.6 W
a₁ will shine brighter because of the higher power.
- oldschoolLv 71 month ago
P = V²/R so R = V²/P = Uo²/P
The current i = Uo/(Uo²/40 + Uo²/60) =
Uo/(60Uo²/2400 + 40Uo²/2400) = 2400Uo/Uo²(60+40)
= 24/Uo = i in the ckt with the two resistors in series with source Uo. Thus the power in the 40W
= 24²/Uo² *Uo²/40 = 24²/40 = 14.4W
In the 60W P = 24²/60 = 9.6W so the 40W bulb is brighter.
- PhilomelLv 71 month ago
Each lamp will have 1/2 design voltage.
The 40W a1 will dissipate ~10W.
The 60W a2 will dissipate ~15W.
The 60W bulb a2 will be brighter.
- oubaasLv 71 month ago
R1 = Uo^2/40
R2 = Uo^2/60
I = Uo/(R1+R2) = Uo*120/5Uo^2 = 24/Uo
P1 = R1*I^2 = Uo^2/40*24^2/Uo^2 = 14,4 watt
P2 = R2*I^2 = Uo^2/60*24^2/Uo^2 = 9,6 watt
total P = 24 watt
or more simply :
equivalent power in series is the parallel of the powers, i.e. 60 // 40 = 24 watt
P1 = P*a1/(a1+a2) = 24*60/100 = 14,4 watt
P2 = Pa2/(a1+a2) = 24*40/100 = 9,6 watt
a1 will shine more than a2
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- billrussell42Lv 71 month ago
filament lamps are very non-linear vs voltage, so this cannot be solved.
BUT, if I assume they are linear...
power = voltage²/resistance
for the first, 40 = U₀²/R₁
for the second, 60 = U₀²/R₂
R₁ = U₀²/40
R₂ = U₀²/60
note that R₂ < R₁
now put them in series. Use voltage divider rule.
U₁ = U₀R₁/(R₁+R₂)
U₂ = U₀R₂/(R₁+R₂)
power = U²/R
P₁ = (U₀R₁/(R₁+R₂))²/R₁
P₂ = (U₀R₂/(R₁+R₂))²/R₂
P₁ = R₁(U₀/(R₁+R₂))²
P₂ = R₂(U₀/(R₁+R₂))²
now compare the two.
(U₀/(R₁+R₂))² term is same, so power is proportional to resistance
since R₂ < R₁, that means P₂ < P₁ and A₁ is brightest