96. Si and Cu are cooled to a temperature of 300 K, then resistivity?​​

1. 1. For Si increases and for Cu decreases

   
   
   

   2. ​For Cu increases and for Si decreases ​

   
   
   

   3. Decreases for both Si and Cu ​

   
   
   

   4. Increases for both Si and Cu

   
   
   

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1. View Hint View Answer Discuss in Forum

   Conductivity of semiconductor increases with increase in temperature while conductivity of metal decreases with increase in temperature.
   

   Correct Option: B

   Conductivity of semiconductor increases with increase in temperature while conductivity of metal decreases with increase in temperature.
   

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97. ​The resistivity (specific resistance) of a copper wire​​

1. 1. increases with increase in its temperature ​

   
   
   

   2. decreases with increase in its cross-section ​

   
   
   

   3. ​increases with increase in its length ​

   
   
   

   4. increases with increase in its cross-section

   
   
   

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1. View Hint View Answer Discuss in Forum

   Resistivity of copper wire increases with increase in temprature as ρ_t = ρ₀(1 + αt)
   Copper being a metal has positive coefficient of resistivity.
   

   Correct Option: A

   Resistivity of copper wire increases with increase in temprature as ρ_t = ρ₀(1 + αt)
   Copper being a metal has positive coefficient of resistivity.
   

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98. A 6 volt battery is connected to the terminals of the three metre long wire of uniform thickness and resistance of 100 ohm. The difference of potential between two points on the wire separated by a distance of 50 cm will be​​

1. 1. 1.5 volt

   
   
   

   2. 3 volt

   
   
   

   3. 3 volt

   
   
   

   4. ​1 volt

   
   
   

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1. View Hint View Answer Discuss in Forum

   ​R α l ​
   For 300 cm, R = 100 Ω
   

   For 50 cm, R' -	100	× 50 =	50	Ω
   	300		3

   
   ∴ IR = 6
   

   ⇒ IR' =	6	× R' =	6	×	50	= 1 volt.
   	R		100		3

   
   

   Correct Option: D

   ​R α l ​
   For 300 cm, R = 100 Ω
   

   For 50 cm, R' -	100	× 50 =	50	Ω
   	300		3

   
   ∴ IR = 6
   

   ⇒ IR' =	6	× R' =	6	×	50	= 1 volt.
   	R		100		3

   
   

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99. The electric resistance of a certain wire of iron is R. If its length and radius are both doubled, then​​

1. 1. ​the resistance and the specific resistance, will both remain unchanged ​

   
   
   

   2. ​the resistance will be doubled and the specific resistance will be halved ​

   
   
   

   3. the resistance will be halved and the specific resistance will remain unchanged ​

   
   
   

   4. ​the resistance will be halved and the specific resistance will be doubled
      

   
   
   

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1. View Hint View Answer Discuss in Forum

   R =	ρ l1	, now l2 = 2l1
   	A1

   
   A₂ = π(r₂)² = π (2r₁)² = 4π r₁​² = 4A₁
   

   ∴ R2 =	ρ (2 l1)	=	ρ l1	=	R
   	4 A1		2 A1		2

   
   ∴ Resistance is halved, but specific resistance remains the same.
   

   Correct Option: C

   R =	ρ l1	, now l2 = 2l1
   	A1

   
   A₂ = π(r₂)² = π (2r₁)² = 4π r₁​² = 4A₁
   

   ∴ R2 =	ρ (2 l1)	=	ρ l1	=	R
   	4 A1		2 A1		2

   
   ∴ Resistance is halved, but specific resistance remains the same.
   

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100. ​A wire of a certain material is stretched slowly by ten per cent. Its new resistance and specific resistance become respectively:​

1. 1. 1.2 times, 1.3 times

   
   
   

   2. 1.21 times, same ​

   
   
   

   3. both remain the same

   
   
   

   4. 1.1 times, 1.1 times

   
   
   

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1. View Hint View Answer Discuss in Forum

   Resistance of a wire is given by R = ρ	l
   	A

   
   

   If the length is increased by 10% then new length l' = l +	1	=	11	l
   	10		10

   
   In that case, area of cross-section of wire would decrease by 10% ​
   ∴ New area of cross-section
   
   Thus the new resistance increases by 1.21 times. The specific resistance (resistivity) remains unchanged as it depends on the nature of the material of the wire.
   

   Correct Option: B

   Resistance of a wire is given by R = ρ	l
   	A

   
   

   If the length is increased by 10% then new length l' = l +	1	=	11	l
   	10		10

   
   In that case, area of cross-section of wire would decrease by 10% ​
   ∴ New area of cross-section
   
   Thus the new resistance increases by 1.21 times. The specific resistance (resistivity) remains unchanged as it depends on the nature of the material of the wire.
   

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