Question

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.​

Answer 1

resistance of 1st lamp, R1 = V1²/P1 = (220)²/100
= 484 ohm
resistance of 2nd lamp, R2 = V2²/P2 = (220)²/200
= 242 ohm.

if lamps are connected in series ,
Req = R1 + R2 = 484 + 242 = 726 ohm
so, I = V/Req = 220/726 = 20/66 Amp = 10/33
= 0.3 amp

if lamps are connected in parallel combination,
Req = R1R2/(R1 + R2)
= 484 × 242/(484 + 242)
= 484 × 242/726
= 44 × 242/66
= 4 × 242/6
= 484/3 ohm

so, I = V/Req = 220/(484/3) = 660/484
= 60/44 = 15/11 = 1.36 Amp



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Answer 2

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Here,

 

P1 = 100 W

P2 = 200W

V = 220 volt

t = 1 hr = 3600 s

We have P = V×I

Current drawn by first lamp I1 = P1/V1 =  40/220

Current drawn by 2nd lamp I2 = P2/V2 =  60/220

Total current drawn  = I1 + I2 = 40/220 + 60/220

  = 10/22 = 0.45A

Total power of the two lamps = 60 + 40 = 100W

Now E = P×t = 100×3600

  = 3.6×105 J