Two lamps, one rated 100 W at 220 V and the other 200 W at 220V are connected (i) in series and (ii) in parallel to electric main supply of 220V. Find the current drawn in each case.
Answers
Lamp1, R1 = V1²/P1 = (220)²/100
=484 ohm
Lamp2, R2 = V2²/P2 = (220)²/200
=242 ohm
In series
Req = R1 + R2 = 484 + 242 = 726 ohm
I=V/Req = 220/726 = 20/66 Amp = 10/33
= 0.30A
in parallel
Req=R1R2/(R1 + R2)
= 484*242/(484 + 242)
= 484*242/726
= 4*242/6
= 484/3 ohm
so, I =V/Req =220/(484/3)= 660/484
=1.36 A
We know the Formula,
R = V²/P
Now, For First Lamp, V = 220 V, and P = 100 W.
∴ R₁ = 220²/100
∴ R₁ = 484 Ω
For Second Lamp, V = 220 V, P = 200 W,
∴ R₂ = 220²/200
∴ R₂ = 484/2
∴ R₂ = 242 Ω
(i) When they are connected in series,
R = R₁ + R₂ = 484 + 242
R = 726 Ω
Using Ohm's law,
V = IR
∴ 220 = I × 726
∴ I = 0.3030 A.
(ii) When they are connected in Parallel,
1/R = 1/R₁ + 1/R₂
∴ 1/R = 1/484 + 1/242
∴ R = 161.3 Ω
Again using the Ohm's law,
I = V/R = 220/161.3
I = 1.36 A.
Hope it helps.