Question

Question 24:
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.
(a) Draw a circuit diagram to show the connections.
(b) Calculate the current drawn from the electric supply.
(c) Calculate the total energy consumed by the two lamps together when they operate for one hour.

Lakhmir Singh Physics Class 10

Answer 1

Answer:

(a): The circuit diagram has been shown.

(b): The current drawn from the electric supply = 0.45 A.

(c): The total energy consumed by the two lamps = $3.564\times 10^5\ J$.

Explanation:

Given:

Power rating of first lamp, $P_1$ = $40\ W$.

Power rating of second lamp, $P_2$ = $60\ W$.

Voltage supply, $V$ = $220\ V$.

Assumptions:

$I_1,\ I_2$ = current passing through first and second lamps respectively.

$I$ = current drawn from the electric supply.

Part (a):

The circuit diagram has been attached below.

Part (b):

The power consumed by an electrical element is given as

$P = VI\\\Rightarrow I = \dfrac PV$

Therefore,

$I_1 = \dfrac{P_1}{V} = \dfrac { 40}{220} = 0.18\ A.\\I_2 =\dfrac{P_2}{V} = \dfrac { 60}{220} = 0.27\ A.$

Using Kirchoff's current law,

$I = I_1 + I_2 \\= 0.18+0.27\\=0.45\ A.$

Part (c):

The total power consumed by the two lamps is given by

$P = VI = 220\times 0.45 = 99\ W.$

The power consumed by the lamps is the amount of total electrical energy consumed by the lamps per unit time.

Therefore,

$P = \dfrac Et\\\Rightarrow E = P\ t$

For $t = 1\ \rm hour = 3600\ seconds$,

$E = P\ t\\= 99\times 3600\\= 3.564\times 10^5\ J.$

Answer 2

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