An electric lamp of 100 ohm, a toaster of resistance 50 ohm, and a water filter of resistance 500 ohm are connected in parallel to a 220 V source. What is the resistance of an electric iron connected to the same source that takes as much current as all three appliances, and what is the current through it?

When resistors are connected in parallel, the reciprocal of the equivalent resistance (Req) is equal to the sum of the reciprocals of the individual resistances. The formula for resistances in parallel is given by:

1/Req = 1/R₁ + 1/R₂ + 1/R₃ + . . .

For the given situation:

1/Req = 1/100 + 1/50 + 1/500

Now, let’s calculate Req:

1/Req = 1/100 + 2/100 + 1/500

1/Req = 3/100 + 1/500

1/Req = 15/500 + 1/500

1/Req = 16/500

Req = 500/16

Req = 31.25Ω
So, the equivalent resistance of the electric lamp, toaster, and water filter connected in parallel is 31.25Ω.

Now, if the electric iron is to draw the same current as all three appliances combined, we can use Ohm’s Law ( V= I ⋅R) to find the current (I) through the equivalent resistance:

I = V /Req
​
I = 220/31.25
​
I ≈7.04A

Therefore, the resistance of the electric iron connected to the same source is 31.25Ω, and the current through it is approximately 7.04A.