31. 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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32. ​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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33. 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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34. A wire of resistance 4 Ω is stretched to twice its original length. The resistance of stretched wire would be​​

1. 1. ​4 Ω ​

   
   
   

   2. 8 Ω ​

   
   
   

   3. 16 Ω

   
   
   

   4. ​2 Ω

   
   
   

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1. View Hint View Answer Discuss in Forum

   Resistance R =	ρl
   	A

   
   ∵ l' = 2l
   

   ∴ A' =	A
   	2

   
   

   ∴ R'ρ	2l	= 4R = 4 × 4Ω = 16Ω
   	A

   
   Therefore the resistance of new wire becomes 16 Ω

   Correct Option: C

   Resistance R =	ρl
   	A

   
   ∵ l' = 2l
   

   ∴ A' =	A
   	2

   
   

   ∴ R'ρ	2l	= 4R = 4 × 4Ω = 16Ω
   	A

   
   Therefore the resistance of new wire becomes 16 Ω

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35. ​The resistance of a wire is 'R' ohm. If it is melted and stretched to 'n' times its original length, its new resistance will be :-​​

1. 1. R/n

   
   
   

   2. n²R

   
   
   

   3. R/n²

   
   
   

   4. nR

   
   
   

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1. View Hint View Answer Discuss in Forum

   We know that, R =	ρl
   	A

   
   

   or R =	ρl²	⇒ R ∝ l²
   	Volume

   
   According to question l₂ = nl₁
   

   	R2	=	n²l1²
   	R1		l1²

   
   

   or,	R2	n²
   	R1

   
   ⇒ R₂ = n²R₁

   Correct Option: B

   We know that, R =	ρl
   	A

   
   

   or R =	ρl²	⇒ R ∝ l²
   	Volume

   
   According to question l₂ = nl₁
   

   	R2	=	n²l1²
   	R1		l1²

   
   

   or,	R2	n²
   	R1

   
   ⇒ R₂ = n²R₁

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