SATHEE: Current Electricity 3 Question 1

Current Electricity 3 Question 1

1. One kilogram of water at $20^{\circ} C$ is heated in an electric kettle whose heating element has a mean (temperature averaged) resistance of $20 Ω$ . The rms voltage in the mains is $200 V$ . Ignoring heat loss from the kettle, time taken for water to evaporate fully, is close to

[Specific heat of water $= 4200 J / (k g^{\circ} C)$ , Latent heat of water $= 2260 k J / k g$ ]

(2019 Main, 12 April II)

(a) $16 m i n$

(b) $22 m i n$

(d) $10 m i n$

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Solution:

Heat required by water for getting hot and then evaporated is

$Δ Q = m s Δ T + m L$

Here, $m = 1 k g, Δ T = 100^{\circ} - 20^{\circ} = 80^{\circ} C$ ,

$s = 4200 J k g^{- 1}^{\circ} C^{- 1}, L = 2260 \times 10^{3} J k g^{- 1}$

So, heat required is

$\begin{aligned} Δ Q & = 1 \times 4200 \times 80 + 1 \times 2260 \times 10^{3} \\ = 336 \times 10^{3} + 2260 \times 10^{3} \\ = 2596 \times 10^{3} J \end{aligned}$

This heat is provided by a heating coil of resistance $R = 20 Ω$ connected with AC mains $V_{rms} = 200 V$

So, heat supplied by heater coil is

$Q = P t = \frac{V_{r m s}^{2}}{R} \times t$

where, $P =$ power and $t =$ time.

$\begin{aligned} = \frac{(200)^{2}}{20} \times t \\ = 2 \times 10^{3} \times t \end{aligned}$

Substituting the value of heat from Eq. (ii), we get

$\begin{aligned} t & = \frac{2956 \times 10^{3}}{2 \times 10^{3}} s \\ = \frac{2956}{2 \times 60} m i n = 24.63 m i n \end{aligned}$

Nearest answer is $22 m i n$ .

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Current Electricity 3 Question 1

1. One kilogram of water at $20^{\circ} C$ is heated in an electric kettle whose heating element has a mean (temperature averaged) resistance of $20 Ω$ . The rms voltage in the mains is $200 V$ . Ignoring heat loss from the kettle, time taken for water to evaporate fully, is close to

Solution:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Current Electricity 3 Question 1

1. One kilogram of water at 20∘C is heated in an electric kettle whose heating element has a mean (temperature averaged) resistance of 20Ω. The rms voltage in the mains is 200V. Ignoring heat loss from the kettle, time taken for water to evaporate fully, is close to

Solution:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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1. One kilogram of water at $20^{\circ} C$ is heated in an electric kettle whose heating element has a mean (temperature averaged) resistance of $20 Ω$ . The rms voltage in the mains is $200 V$ . Ignoring heat loss from the kettle, time taken for water to evaporate fully, is close to