An electric lamp of 100 Ohms, a toaster of resistance of 50 Ohms, and a water filter of resistance of 500 Ohms 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?

By Ritesh|Updated : November 11th, 2022

The resistance of an electric iron connected to the same source that takes as much current as all three appliances is 31.25 Ω and the current through it is 7.04 A. Steps to find the resistance of an electric iron connected:

Step 1: Given that,

Resistance of electric lamp (R1) = 100Ω

Resistance of toaster (R2) = 50Ω

Resistance of water filter (R3) = 500Ω

Source potential difference (V) = 220V

The following illustration shows how the three resistors are linked in parallel.

three resistors are linked in parallel

Step 2: determining the electron iron's resistance

The formula for calculating total resistance (R) is presented below.

1/R = 1/R1 + 1/R2 + 1/R3

Now substituting the given values in the above equation, we get:

1/R = 1/100 + 1/50 + 1/500

= (5 + 10 + 1)/500

In simplification we get the:

= 16/100

When we use cross-multiplication, we obtain:

R = 500/16 Ω

R = 31.25 Ω

Step 3: Using the electric iron to detect the electric current

As stated by Ohm's law,

V ∝ I or V = IR

Now on rearranging, we get:

R = V/I

Now by substituting the values in the above formula, we get:

500/16 = 220/I

I = 220 X 16/500

I = 7.04 A

Hence, the resistance is 31.25 Ω and the current is 7.04 A.

Summary:

An electric lamp of 100 Ohms, a toaster of resistance of 50 Ohms, and a water filter of resistance of 500 Ohms 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?

An electric lamp of 100 Ohms, a toaster of resistance of 50 Ohms, and a water filter of resistance of 500 Ohms are connected in parallel to a 220 V source. The resistance of an electric iron connected to the same source that takes as much current as all three appliances is 31.25 Ω and the current through it is 7.04 A.

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