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

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.

Answer 2

HI !

Power = P = 100 W
Voltage = V = 220v
Resistance = R

P = V²/R
100 = 220 ×220/R
R  = 220 × 220/100
     = 484 Ω
==========================
Power = P = 60 W
Voltage = V = 220v
Resistance = R

P = V²/R
60 = 220 × 220/R
R = 220× 220/60
    = 806.7 Ω
=========================
As the resistors are connected in parallel , 
total resistance = 1/R

1/R = 1/484 + 1/806.7
      =  806.7 + 484/484×806.7
      = 1290.7/390442.8
R = 390442.8/ 1290.7 = 302.5 ohms
    
  Total resistance = 302.5 Ω


I = current

V = IR
220 = I × 302.5

I = 220/302.5
   = 0.73 A

The current drawn is 0.73 A