Question

50 lamps each of resistance 100 ohm are connected in parallel across a 220 volts main.Find(a)the power consumed in Watts,and(b)the cost of 0perating the lamps for 20 hours at 10 paise per kWh.

Answer 1

The equivalent resistance of 50 lamps,r= 2 ohm
current,i=220/2=110
power consumed=i^2.r=(110^2)*2=12100*2=24200Wh
=24.2kwh
cost=24.2*20*60*60*10/100=174240 rupees

Answer 2

Answer:

The power consumed is 24.2 kW and the cost is 242 rupees.

Explanation:

Given that,

50 lamps each of resistance 100 ohm are connected in parallel across a 220 volts main.

The equivalent resistance is

$\dfrac{1}{R}=\dfrac{1}{R_{1}}+\dfrac{1}{R_{2}}+\dfrac{1}{R_{3}}.......\dfrac{1}{R_{50}}$

$\dfrac{1}{R}=\dfrac{1}{100}+\dfrac{1}{100}+\dfrac{1}{100}.......\dfrac{1}{100}$

$\dfrac{1}{R}=\dfrac{50}{100}$

$R = 2\ \Omega$

(I). The power consumed will be

$P=\dfrac{V^2}{R}$

$P=\dfrac{(220)^2}{2}$

$P=24200\ W$

$P=24.2 kW$

The total power consumed by 50 lamps

$P = 24.2\times50=121000\ W$

(II). The cost of operating the lamps for 20 hours at 10 paise per kWh is

Cost =$121\times20\times0.1$

Cost = 242 rupees

Hence, The power consumed is 24.2 kW and the cost is 242 rupees.