Electric Current Test

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Electric Current Test - 22

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Weekly Quiz Competition

Question 1
1 / -0

A brass disc and a carbon disc of same radius are assembled alternatively to make a cylindrical conductor. The resistance of the cylinder is independent of the temperature. The ratio of thickness of the brass disc to that of the carbon disc is ______. α is temperature coefficient of resistance & Neglect linear expansion

A

B

C

D

Solution
Question 2
1 / -0

Out of the following which is not a poor conductor ?

A
Cast iron

B
Copper

C
Carbon

D
Tungsten

Solution

J= {J0[(x/R)-1] 0 ≤ x ≤ R/2, {J0(x/R) R/2 ≤ x ≤ R
We know that,
J=current/area
⇒ current=J Area
Current= J1A1 +J2A2
=J0{(x/R)−1}x(2πxdx)+J0 (x/R)(2πxdx)
=∫0R/2J0{(x/R)-1} x (2πxdx) + =∫0R/2J0 x 2π (x2/R)dx
= J0×2π∫0R/2 {(x2/R)−x}dx + (J0×2π/R) ∫RR/2 x2dx
⇒ i=J0×2π [(x3/3R)-(x2/2)] R/2 + (J0×2π/R) [x3/3]R2/R
⇒i=J0×2π [(R2/24)−(R2/8)]+ (J0×2π/R)[(R3/3)-(R3/24)]
=J0×2π(−2R2/24)(J0×2π/R)[7R3/24]
i =(5/12)πJ0R2
Question 3
1 / -0

Under what condition current passing through the resistance R can be increased by short circuiting the battery of emf E₂. The internal resistances of the two batteries are r₁ and r₂ respectively.

A
E₂r₁ > E₁(R + r₂)

B
E₁r₂ > E₂(R + r₁)

C
E₂r₂ > E₁(R + r₂)

D
E₁r₁ > E₂ (R + r₁)

Solution

The current through the circuit before the battery of emf E2 is short circuited, is
i₁=(E₁+E₂)/r₁+r₂+R ...(i)
After short circuiting the battery of emf E₂, current through the resistance R would be
i2= E₁/R+r₁ ...(ii)
Since, from equation (i) and (ii), we get
i2>i1
∴ E₁/R+r₁ > E₁+E₂/R+r₁+r₂
This gives E₁r₂>E₂(R+r₁)
Question 4
1 / -0

ABCD is a square where each side is a uniform wire of resistance 1Ω. A point E lies on CD such that if a uniform wire of resistance 1W is connected across AE and constant potential difference is applied across A and C then B and E are equipotential.

A

B

C

D

Solution

Wire of resistance =1Ω
Keeping in view that, ABCD is a square where each side is uniform wire of resistance 1Ω. If a uniform wire of resistance 1Ω is connected across AE and a potential difference is applied across A and C, the points B and E will be equipotential; a point E on CD is CE/ ED =√2/1
∴ CE:ED= √2:1
Question 5
1 / -0

Two current elements P and Q have current voltage characteristics as shown below :
Which of the graphs given below represents current voltage characteristics when P and Q are in series.

A

B

C

D
Question 6
1 / -0

Power of battery in resistor appears as

A
power consumption

B
power dissipation

C
power resistance

D
both a and b
Question 7
1 / -0

A simple circuit contains an ideal battery and a resistance R. If a second resistor is placed in parallel with the first.

A
The potential across R will decrease

B
The current through R will decreased

C
The current delivered by the battery will increase

D
The power dissipated by R will increased.

Solution

When a resistor is added parallel to other resistor in circuit it results in the reduction of overall resistance, since there are multiple pathways by which charge can flow. adding another resistor in a separate branch provides another pathway by which to direct charge through the main area of resistance within the circuit. This decreased resistance resulting from increasing the number of branches will have the effect of increasing the rate at which charge flows i.e. the current.
Question 8
1 / -0

Consider the circuit shown in the figure

A
The current in the 5 W resistor is 2A

B
The current in the 5W resistor is 1A

C
The potential difference V_A _ V_B is 10 V

D
The potential difference V_A _ V_B is 5V

Solution

R_AD=1/(1/10)+(1/3+4+3)=5Ω
R_CB=1/(1/10)+(1/3+5+2)= 5Ω
i=28/5+5+4=2A
current through 5Ω is 2A
R_CADB=R_CB
⇒i_CA=i_CB=i/2=1A
V_CA=1x3=3V
V_CB=1x10=10V
V_AB=VCB-VCA=10-3
V_A-V_B=7V
Question 9
1 / -0

A copper wire of radius 0.1 mm and resistance 1 kW is connected across a power supply of 20 V. How many electrons are transferred per second between the supply and the wire at one end ?

A
1.25 x 10^-17

B
1.25

C
6.23 x 10^-23

D
None of these
Question 10
1 / -0

A car has a fresh storage battery of emf 12 V and internal resistance 5.0 × 10^-2W. If the starter draws a current of 90 A, what is the terminal voltage of the battery when the starter is on ?

A
7.5 V

B
5 V

C
12 V

D
None of these