Question

A bulb is rated at 200V - 100W. What is the resistance ? Five such bulbs burn for 4 hours. What is the electrical energy consumed ? Calculate the cost if the rate is ₹ 4.60 per unit.​

Answer 1

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Solution. (a) Calculation of Resistance. Here we know the voltage and power of the bulb. So, the resistance can be calculated by using the formula :

$\: \: \: \: \: \: \: P = \frac{v {}^{2} }{r} \\ \\ Here, \: Power, \: P = 100 \: watts \\ \\ \: \: \: \: \: \: \: \: \: Voltage, \: V = 200 \: volts \\ \\ And, \: Resistance, \: R = \ \ \: ? \\ (to \: be \: calculated \: ) \\ \\ Now, \: putting \: these \: values \: in \: the \\ above \: formula \: we \: get : \\ \\ 100 = \frac{(200) {}^{2} }{R} \\ \\ 100 \: R = 40000 \\ \\ And, \: R = \frac{40000}{100} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: = 400 \: ohms \\ \\ (b) \: Calculation \: of \: Electrical \: Energy \\ Consumed. \: the \: Electrical \: energy \\consumed \: in \: kilowatts - hours \\can \: be \: calculated \: by \: using \: the \: \\ formula: \\ \\ \: \: E = P \times T \\ \\ Here, \: power, \: P = 100 \: watts \\ \\ \: \:= \frac{100}{1000} kilowatts \\ \\ \: \: = 0.1 \: kilowatt \: \: \: \: ...(1) \\ \\ And, \: time, \: T = 4 \: hours \: \: \: \: ...(2) \\ \\ So, \: Energy \: consumed \: by \: 1 \: bulb \\ \: \: = 0.1 \times 4 \\ \\ \: \: = 0.4 \: kilowatts - hours \\ \\ And, \: energy \: consumed \: by \: 5 \: bulbs \: \\ \: \: = 0.4 \times 5 \\ \\ \: \: = 2 \: kilowatts - hours \\ \\ Thus, \: the \: total \: electrical \: energy \: \\ consumed \: is: \\ (2 \: kilowatts - hours )or (2 \: units). \\ \\ (c) \: calculation \: of \: cost \: of electrical \: \\ \:energy. We \: have \: been \: \\ given \: that: \\ \\ cost \: of \: 1 \: unit \: of \: electricity \\ \: \: = 4.60 \: rs \\ \\ So, \: \: cost \: of \: 1 \: of \: electricity \\ \: \: = 4.60rs \times 2 \: rs \\ \\ \: \: = 9.20 rs \: \: \: \: \: \: \: (Answer)$

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Answer 2

$\huge\fbox\orange{\underline{Question:–}}$

An electric bulb is rated at 200w-100w what is the resistance of 5 such bulbs burn for 4 hours. What is the electrical energy consumed. Calculate the cost if the rate is 50 paise per unit.

$\huge\fbox\orange{\underline{Answer:–}}$

Using, P = $\large{V²}{R}$

we get R = $\large{V²}{P}$

= $\large{(200)²}{100}$

= 400

Energy consumed = P x t

= 100 x 4

= 400 Wh

= 0.4 kWh

Cost at the rate of 50 paise per unit

= Rs (0.50 x 0.4)

= Rs 2

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