fifty lamps each of 100ohm are connected in parallel across a 220v main. find the power consumed in watts,and the cost of operating the lamps for 20hours at 10paise per kWh

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Solution

Here
Potential difference = 220 V
t = 20 hrs
rate = 10p /kWh
r = 100Ω
n = 50
Total resistance in parallel
1/R_|| = 1/100 + 1/100 + …+ 1/100 (50 terms)
=> 1/R_|| = 50/100
=> R_|| = 2Ω
P = V²/R
=> P = (220)²/2
=> P = 24200 W
=> P = 24.2 kW
If lit for 20 hrs power consumption becomes
P = 24.2 × 20 kWh
= 484 kWh
Cost per kWh = 0.10 INR
Total cost = 0.10 × 484
= 48.4 INR

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