Question

Two lamps one rated 100w at 220v and the other 200w at 220v are connected I series and 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

Answer 2

Given:

Lamp 1,

Voltage = 100 w

Potential = 220 v

Lamp 2,

Voltage = 200 w

Potential = 220 v

To find:

The current

Solution:

To find resistance,

Resistance = ( Voltage )^2 / Potential

Substituting.

Resistance for lamp 1 = ( 220 )^2 / 100

Resistance for lamp 1 = 484 Ω

Resistance for lamp 2 = ( 220 )^2 / 200

Resistance for lamp 2 = 242 Ω

In a series,

Current = Voltage / Resistance

Here,

Resistance = Resistance for lamp 1 + Resistance for lamp 2

484 + 242

Resistance = 726 Ω

Hence,

Current = 220 / 726 = 0.3 Amp

In parallel,

Resistance  = Resistance for lamp 1 * Resistance for lamp 2/( Resistance for lamp 1 + Resistance for lamp 2 )

484 × 242 / ( 484 + 242 )

= 4 × 242/6

Resistance = 484/3 Ω

Current = 220 / ( 484 / 3 )

Hence,

Current = 1.36 Amp