10. (a) Write Joule's law of heating. (b) Two lamps, one rated 100 W; 220 V, and the other 60W; 220 V, are connected in parallel to Electric mains supply. Find the current drawn by two bulbs from the line, if the supply voltage is 220 V.
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a) Joule's law of heating can be defined as when current passes through a conductor, heat is generated. It is also known as Ohmic heating or resistive heating.
P = I² R = V²/R
Where P is in watts, I is in Amperes, R is in ohms and V is volts.
b) firstly we would find the resistance of the lamps.
P₁ = 100 W
V₁ = 220 V
R ₁ = V₁²/P₁ = 484 Ω
P₂ = 60 W
V₂ = 220 V
R₂ = V₂²/P₂ = 806.67 Ω
The lamps are connected in parallel. Equivalent resistance =
R = (R₁×R₂)/(R₁+R₂) = (484 Ω×806.67 Ω)( 484 Ω+806.67 Ω) = 302.5 Ω
From Ohm's law, current drawn is given by:
I = V /R = 220 V/ 302.5Ω = 0.727 A
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