Question

Two lamps, one rated 80 at 220 and the other 100 at 220 , are connected in parallel to the

electric supply at 220 . (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.​

Answer 1

$\bf\underline{\underline{\orange{ Given:-}}}$

P1 (Power for first lamp) = 80 W

P2 (Power for second lamp) = 100 W

V (Potential difference) = 220 V

$\bf\underline{\underline{\orange{ Find:-}}}$

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 the system operate for one hour.

$\bf\underline{\underline{\orange{ Solution:-}}}$

Resistance R of each lamp from given power P and operating voltage V is obtained from the relation,  

P = ( V2 / R )  ....................... (1)

  Hence resistance of 100W, 220 V lamp = (220×220)/100 = 484 Ω

 

Resistance of 200W, 220 V lamp = (220×220)/200 = 242 Ω  

when lamps are connected in series , equivalenet resistance = 484+242 = 726 Ω

  Hence current drawn by lamps that are connected in series = 220/726 = 0.3 A

  When lamps are connected in parallel, each lamp draws current independenly as per its wattage.  

Current drawn by 100 W lamp = 100/220 = 0.45 A Current drawn by 200 W lamp = 200/220 = 0.91A

Hence, total current drawn by lamps when they are connected in parallel = 0.45+0.91 = 1.36 A

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Answer 2

Concept:

In a complete electrical circuit, the current is the rate at which electrons move past a certain point.

Given:

Two bulbs with powers $80$ and $100$ watts are connected in parallel with an electric supply at $200$ volts.

Find:

The circuit diagram of the connections, the current drawn from the electric supply, and the total energy consumed by the two lamps together.

Solution:

The power of the first lamp, $P_1=80W$

The power of the second lamp, $P_2=100W$

The potential difference, $V=220$ volts.

The formula for power is given as P = VI, where V and I are the voltages and current.

The current passing through the first lamp,

$I_1=\frac{P_1}{V}$

$I_1=\frac{80}{220} =\frac{4}{11}A$

The current passing through the second lamp,

$I_2=\frac{P_2}{V}$

$I_2=\frac{100}{220}=\frac{5}{11}A$

The lamps are connected in parallel and the current is divided equally.

The net current is:

$I=I_1+I_2\\I=\frac{4}{11}+\frac{5}{11}=\frac{9}{11}A$

$I=0.82A$

The energy consumed by the first lamp in one hour is:

$=P\times t=80\times 1h=80Wh$

The energy consumed by the second lamp in one hour is:

$=100\times 1h=100Wh$

The total energy consumed is $80+100=180Wh$.

The current drawn is $0.82A$ and the total energy consumed by the two lamps together in one hour is $0.18kWh$.

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