In a house having 120v circuit, the following light bulbs were turned on 40w,60w,75w.
Calculate the equivalent resistance of the bulbs
Assuming that all these light bulbs were connected in parallel.
All the bulbs are subject to the same voltage 120 V. The current from the source voltage is split between the three bulbs in the relation,
i = i1 + i2 + i3
And
i = V/R
Where V is the source voltage = 120 V
And R is the equivalent resistance of the three light bulbs. We have ,
W1 = 40 W
W2 = 60 W
W3 = 75 W
Individually,
i1 = W1/V = 40/120 = 1/3 A.
I2 = W2/V = 60/120 = 1/2 A.
I3 = W3/V = 75/120 = 5/8 A.
Total current is,
i = i1 + i2 + i3
i = 1/3 + 1/2 + 5/8 = 5/6 + 5/8 = 5(1/6 + 1/8) = 5(4 + 3)/24 = 35/24
i = 35/24 A.
Using i = V/R,
R = V/i = 120 / (35/24) = 120*24/35 = 82.2857
Equivalent Restance = 82.28 Ω