Question

two lamps one rated 100w at 220v and the other 200w at 220v are connected (i) in series and (ii) in parallel to the electric main supply of 220v. Find the current drawn in each case.
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Answer 1

Explanation:

power =work done/time taken

P=w/t

we know v=w/q

w=vq

P=vq/t

q/t=i

P=VI

i=v/r

P=V^2/R

R=V^2/P

R1=v^2/p1

R1=220×220/100

R1=484 ohm

R2=V^2/P1

R2=220×220/200

R2=242 ohm

1. in series Reff=R1+R2

=484+242

Reff=726 ohm

i=v/R

i=220/726

i=0.30A

2.in parllel Reff =R1.R2/R1+R2

Reff=484/3 ohm

i=220/(484/3)

i=1.3A

Answer 2

P 1 =100

V 1 = 220 V

we know that ,

P 1=V²1/R 1

R 1 = V 1 ² /P 1

R 1= 48400/100

R 1= 484 ohm

R 2= V 2 ²/ P2

R 2 = 48400/200

R 2= 242 ohm

(1) R 1 and R 2 are connected in series

Rs = R 1 +R 2

R s = 242 +484

Rs = 726

I = V /R

I = 220 / 726

I =0 .30 A

(2) R1 and R 2 are connected in parallel

Rp = R 1 × R2 /R 1 + R 2

R p = 484×242/726

Rp = 161.3 ohms

I = V/R

I = 220 / 161

I =1.36 A