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Two lamps, one rated 40 W at 220 V and the other 60 W at 220 V, are connected in parallel to the electric supply at 220 V- Draw a circuit diagram to show the connections.
- Calculate the current drawn from the electric supply.
- Calculate the total energy consumed by the two lamps together when they operate for one hour.
Given,
Power of 1st lamp, P1 = 40W, Voltage of 1st lamp, V1 = 220V
Power of 2nd lamp, P2 = 60W, Voltage of 2nd lamp, V2 = 220V
(a) Circuit diagram of the connections.
We know that,
$P=V\times I$, where P = Power, V = Voltage, I = Current.
In term of Current I, it can be given as-
$I=\frac{P}{V}$
Now,
Current through 40W lamp = I1 = $\frac{{P}_{1}}{V}$ = $\frac{40}{220}A$
Current through 60W lamp = I2 = $\frac{{P}_{2}}{V}$ = $\frac{60}{220}A$
Total current drawn from the electric supply = $\frac{40}{220}+\frac{60}{220}=0.45A$
(c) Energy consumed by 40W lamp in 1hr, ${E}_{1}={P}_{1}\times t=40\times 1=40Wh$
So, energy consumed by Lamp-1 = $40\times 3.6=144kJ$ $[\because 1Wh=3.6kJ]$
Energy consumed by 60W lamp in 1hr, ${E}_{2}={P}_{2}\times t=60\times 1=60Wh$
So, energy consumed by Lamp-2 = $60\times 3.6=216kJ$ $[\because 1Wh=3.6kJ]$
Total energy consumed = (Energy consumed by Lamp-1 + Energy consumed by Lamp-2) = 144 + 216 = 360kJ
Hence, the total energy consumed by the two lamps together when they operate for one hour is 360kJ.