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CBSE Class 10 Science 2022 Delhi Term II Set 1

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Question : 12 of 15
Marks: +1, -0
(a) List the factors on which the resistance of a uniform cylindrical conductor of a given material depends.
(b) The resistance of a wire of 0.01 cm0.01\text{ cm} radius is 10Ω10\Omega. If the resistivity of the wire is 50×10−8Ω m50 \times 10^{-8} \Omega \text{ m}, find the length of this wire.
OR
(a) What is the meaning of electric power of an electrical? Write its SI unit.
(b) An electric kettle of 2 kW2 \text{ kW} is used for 2 h2 \text{ h}. Calculate the energy consumed in
(i) kilowatt hour and
(ii) joules.
Solution:  
(a) Length of conductor, area of its crosssection and its material are the factors on which the resistance of a uniform cylindrical conductor of a given material depends.
(b)
  R=10 ohm;r=0.01 cm;\;R=10 \text{ ohm} ; r=0.01 \text{ cm} ;
  ρ=50×10−8 ohm   metre   \;\rho=50 \times 10^{-8} \text{ ohm} \;\text{ metre }\;
  R=ρlA=  (50×10−8×l)(3.4142×10−8)\;R=\frac{\rho l}{A}=\;\frac{ (50 \times 10^{-8} \times l) }{ (3.4142 \times 10^{-8}) }
  10=  50×10−8l3.14×10−8\;10=\;\frac{50 \times 10^{-8} l}{3.14 \times 10^{-8}}
  l=  31.450=0.629 m\;l=\;\frac{31.4}{50}=0.629 \text{ m}
OR
(a) Power of electrical device means rate at which electric energy is consumed in an electric circuit. SI unit of power is watt (W).
(b) (i) Energy consumed =W==W= Power ×\times time
=2 kW×2 h=4 kWh=2 \text{ kW} \times 2 \text{ h}=4 \text{ kWh}
(ii) 1 kWh=3.6×106 J1 \text{ kWh}=3.6 \times 10^6 \text{ J};
  So,  4 kWh=4×3.6×106 J=1.44×107 J\;\text{So,}\; 4 \text{ kWh}=4 \times 3.6 \times 10^6 \text{ J}=1.44 \times 10^7 \text{ J}
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