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Question

Bulb is rated as $$200\ V, 100\ W$$. Calculate its resistance. Five such bulbs are lighted for $$4$$ hours daily. Calculated the units of electrical energy consumed per day. What would be the cost of using bulbs per day at the rate of $$Rs. 400$$ per unit?


Solution

We know that for an electric appliance 
$$P=\dfrac {V^2}{R}$$
Resistance will be given by
$$R=\dfrac {V^2}{P}$$
Now, here
$$P=100\ W$$
$$V=200$$ volts
So, $$R=\dfrac {200^2}{100}$$
$$R=\dfrac {40000}{100}=400\ \Omega$$
Thus, resistance of the bulb is $$R=400\ \Omega$$
Now, electric energy consumed will be 
$$E=$$ power of each unit $$\times $$ time.
$$\Rightarrow Energy=P\times t$$
Here
$$P=100\ W$$
$$t==4hours=4\times 60\times 60sec=14400sec\\ $$ 
So,
$$Energy\quad =100\times 14400J=1440000J=1.44\times { 10 }^{ 6 }J$$
Electrical energy consumed by each bulb in Unit 
$$=\frac { 1.44\times { 10 }^{ 6 }J }{ 3.6\times { 10 }^{ 6 }J } =0.4\quad kWh\quad (\because \quad 1kWh=3.6\times { 10 }^{ 6 }J)$$
The total cost of electricity = total unit of energy consumed $$X$$ cost per unit =
Total Cost $$=5\times 0.4\times 400=Rs.800  $$
Thus, total cost of using all  bulbs per day  is $$=Rs. 800$$

Physics

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