Question

Two lamps one rated 100w at 220v and the other200w at22ovare connected (i) in series(ii) in parallel to electric main supply of 220v find the current drawn in each case

Answer 1

P1 = 100W

P2 = 200 W

V = 220 V

P = V²/R

100 = 220²/R1

R1 = 484 Ω

200 = 220²/R2

R2 = 242 Ω

Q i)  In Series Resistance Added

so R1 + R2 = 484 + 242 = 726 Ω

Current = V/R

Current = 220/726 = 0.303 Amp

Q ii ) in parallel Resistance will be

1/R = 1/R1 + 1/R2

1/R = 1/484 + 1/242

484/R = 1+2

R = 484/3 Ω

Current = 220/(484/3)

= 660/484

= 165/121

=  1.3636 Amp

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Answer 2

Answer:

I_series = 0.30 A

I_parallel = 1.36 A

Explanation:

Given :

Two lamps power as 100 W and 200 W at 220 V.

We have resistance formula :

R₁ = 220 × 220 / 100 = 484 Ω

R₂ = 220 × 220 / 200 = 242 Ω

In series combination :

R_net = 484 + 242 Ω

= > 726 Ω

We have ohm's law :

V = I R

I = 220 / 726 A

I = 0.30 A

( ii ) In parallel combination :

1 / R_net = 1 / 484 + 1 / 242 Ω

R_net = 484 / 3 Ω

Given :  V = 220 V

I' = 220 / 484 × 3 A

I' = 1.36 A