an electric lamp of 100 ohm a toaster resistance 50 ohm ,and a water f...
Problem Statement
An electric lamp of 100 ohm, a toaster resistance of 50 ohm, and a water filter of resistance 500 ohm are connected in parallel to a 220V 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?
Solution
To find the resistance of the electric iron, we first need to calculate the total resistance of the appliances connected in parallel.
Calculating Total Resistance
The formula for calculating the total resistance in a parallel circuit is:
1/Rt = 1/R1 + 1/R2 + 1/R3 + ...
Where Rt is the total resistance and R1, R2, R3, etc. are the individual resistances.
Substituting the given values, we get:
1/Rt = 1/100 + 1/50 + 1/500
Simplifying the above equation, we get:
1/Rt = 0.02
Rt = 1/0.02
Rt = 50 ohm
Therefore, the total resistance of the parallel circuit is 50 ohm.
Calculating Current
We know that the voltage across the parallel circuit is 220V. Using Ohm's Law, we can calculate the total current flowing through the circuit as:
I = V/R
I = 220/50
I = 4.4 A
Therefore, the total current flowing through the parallel circuit is 4.4 A.
Calculating Resistance of Electric Iron
To find the resistance of the electric iron, we need to use the formula:
R = V/I
Where R is the resistance, V is the voltage, and I is the current.
Substituting the given values, we get:
R = 220/4.4
R = 50 ohm
Therefore, the resistance of the electric iron is also 50 ohm.
Calculating Current through Electric Iron
Using Ohm's Law, we can calculate the current through the electric iron as:
I = V/R
I = 220/50
I = 4.4 A
Therefore, the current through the electric iron is also 4.4 A.
Conclusion
In conclusion, the resistance of the electric iron is 50 ohm, and the current flowing through it is 4.4 A.