86. Two metal wires of identical dimension are connected in series. If σ₁ and σ₂ are the conductivities of the metal wires respectively, the effective conductivity of the combination is :​​​​

1. 1. 	σ1 + σ2
      	2σ1σ2

   
   
   

   2. 	σ1 + σ2
      	σ1σ2

   
   
   

   3. 	σ1σ2
      	σ1 + σ2

   
   
   

   4. 	2σ1σ2
      	σ1 + σ2

   
   
   

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1. View Hint View Answer Discuss in Forum

   In figure, two metal wires of identical dimension are connected in series
   
   

   Correct Option: D

   In figure, two metal wires of identical dimension are connected in series
   
   

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87. A, B and C are voltmeters of resistance R, 1.5 R and 3R respectively as shown in the figure. When some potential difference is applied between X and Y, the voltmeter readings are V_A, V_B and V_C respectively. Then
    
    

1. 1. V_A ≠ V_B = V_C ​

   
   
   

   2. V_A = V_B ≠ V_C ​

   
   
   

   3. V_A ≠ V_B ≠ V_C

   
   
   

   4. V_A = V_B = V_C

   
   
   

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1. View Hint View Answer Discuss in Forum

   Effective resistance of B and C
   

   =	RB . RC	=		1.5 R × 3R	=	4.5R²	= R
   	RB + RC			1.5R +3R		4.5R

   
   i.e., equal to resistance of voltmeter A.
   
   In parallel potential difference is same so, V_B = V_C and in series current is same ​
   So, V_A = V_B = V_C

   Correct Option: D

   Effective resistance of B and C
   

   =	RB . RC	=		1.5 R × 3R	=	4.5R²	= R
   	RB + RC			1.5R +3R		4.5R

   
   i.e., equal to resistance of voltmeter A.
   
   In parallel potential difference is same so, V_B = V_C and in series current is same ​
   So, V_A = V_B = V_C

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88. The masses of the three wires of copper are in the ratio of 1 : 3 : 5 and their lengths are  in the ratio of 5 : 3 : 1. The ratio of their electrical resistance is​​
    

1. 1. 1 : 3 : 5 ​

   
   
   

   2. 5 : 3 : 1 ​

   
   
   

   3. 1 : 25 : 125 ​

   
   
   

   4. 125 : 15 : 1

   
   
   

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1. View Hint View Answer Discuss in Forum

   R =	ρ l	. But m = πr²ld ∴ πr² =	m
   	πr²		ld

   
   

   ∴ R =	ρl²d	,R1 =		ρl1²d	,R2 =	ρl2²d
   	m			m1		m2

   
   

   R3 =	ρl1²d
   	m3

   
   
   

   R1 : R2 : R3 =	25	:		9	:	1	= 125 : 15 :1
   	1			3		5

   
   

   Correct Option: D

   R =	ρ l	. But m = πr²ld ∴ πr² =	m
   	πr²		ld

   
   

   ∴ R =	ρl²d	,R1 =		ρl1²d	,R2 =	ρl2²d
   	m			m1		m2

   
   

   R3 =	ρl1²d
   	m3

   
   
   

   R1 : R2 : R3 =	25	:		9	:	1	= 125 : 15 :1
   	1			3		5

   
   

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89. The velocity of charge carriers of current (about 1 amp) in a metal under normal conditions is of the order of​​

1. 1. ​a fraction of mm/sec

   
   
   

   2. velocity of light

   
   
   

   3. several thousand metres/second ​

   
   
   

   4. a few hundred metres per second

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: A

   NA

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90. If a wire of resistance R is melted and recasted to half of its length, then the new resistance of the wire will be​​

1. 1. R / 4 ​

   
   
   

   2. R / 2 ​

   
   
   

   3. R ​

   
   
   

   4. 2R

   
   
   

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1. View Hint View Answer Discuss in Forum

   Initial resistance (R₁) = R; Initial length l₁is 1and final length (l₂) = 0.5 l . Volume of a wire = l . A.  Since the volume of the wire remains the same after recasting, therefore l₁. A₁ = l₂ A₂
   
   We also know that resistance of a wire (R)
   

   R = ρ ×	l	.; R ∝	l
   	A		A

   
   

   ∴	R1	=	l1	×	A2	=	l	× 2 = 4
   	R2		l2		A1		0.5l

   
   

   or, R2 =	R1	=	R
   	4		4

   
   [Alt : When wires are drawn from same volume but with different area of cross-section, then
   

   R ∝	1
   	(Area of cross-section)²

   
   

   Correct Option: A

   Initial resistance (R₁) = R; Initial length l₁is 1and final length (l₂) = 0.5 l . Volume of a wire = l . A.  Since the volume of the wire remains the same after recasting, therefore l₁. A₁ = l₂ A₂
   
   We also know that resistance of a wire (R)
   

   R = ρ ×	l	.; R ∝	l
   	A		A

   
   

   ∴	R1	=	l1	×	A2	=	l	× 2 = 4
   	R2		l2		A1		0.5l

   
   

   or, R2 =	R1	=	R
   	4		4

   
   [Alt : When wires are drawn from same volume but with different area of cross-section, then
   

   R ∝	1
   	(Area of cross-section)²

   
   

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