Question

50 lamps each of resistance 100ohm are connected in parallel across a 220 v main .Find (a) the consumed in watts and (b) the cost of operating the lamps for 20hours at 10 paise per kWh.​

Answer 1

Answer:

a=24.2kW b=4840paise

Explanation:

1/Rp=(1/100)*50=1/2

Rp=2 V=220V

P=V^2/R=220*220/2=24.2kW

COST=24.2*10*20=4840PAISE

Answer 2

➭ Question:-

$⟶$50 lamps each of resistance 100ohm are connected in parallel across a 220 v main .Find (a) the consumed in watts and (b) the cost of operating the lamps for 20hours at 10 paise per kWh.

➭ Given :-

$⟶$50 lamps each of resistance 100ohm are connected in parallel across a 220 v main

➭ To find :-

1. The consumed in watts
2. The cost of operating the lamps for 20hours at 10 paise per kWh.

➭ Solution :-

The equivalent resistance is...

$\longrightarrow \tt \: \frac{1}{R} = \frac{1}{ R_{1}} + \frac{1}{ r_{2} } + \frac{1}{ R_{3}} ..... \frac{1}{ R_{50} } \: \: \: \: \: \: \: \: \\ \\ \longrightarrow \tt \frac{1}{R} = \frac{1}{100} + \frac{1}{100} + \frac{1}{100} .... \frac{1}{100} \: \\ \\ \longrightarrow \tt \frac{1}{R} = \frac{50}{100} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \longrightarrow \boxed{ \tt R = 2ohm} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

➝ The power consumed will be:-

$\longrightarrow \rm p = \frac{ {v}^{2} }{r} \: \: \: \: \: \: \: \: \: \: \ \\ \\ \longrightarrow \rm p = \frac{ {200}^{2} }{2} \: \: \: \: \: \: \: \\ \\ \longrightarrow \rm p = 24200w \: \: \\ \\ \longrightarrow \boxed{ \rm p = 24.2kw}$

The total power consumed by 50 lamps..

$\longrightarrow \rm p = 24.2 \times 50 = 12100w$

➝ The cost of operating the lamps for 20hrs at 10 paise per kWh is :-

→ cost = 121 × 20 × 0.1 = 242 rupees

_____________

Hence, the power consumed is 24.2kwh and the cost is 242Rs