Current Electricity Test

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Current Electricity Test - 70

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Weekly Quiz Competition

Question 1
1 / -0

A conductor of resistance $$3 \Omega$$ is stretched uniformly till its length is doubled. The wire is now bent in the form of an equilateral triangle. The effective resistance between the ends of any side of the triangle in $$\Omega$$

A
$$\dfrac{9}{2}$$

B
$$\dfrac{8}{3}$$

C
$$2$$

D
$$1$$

Solution

If we double the length of the conductor$$,$$ then its cross$$-$$sectional area must become half of its original value (since$$,$$ $$volume = area \times length$$ is constant).
Therefore$$,$$ we can say that after stretching the new resistance is $$R' = \rho \dfrac{{2l}}{{A/2}} = 4\rho \dfrac{1}{A} = 4{R_0} = 4 \times 3\Omega = 12\Omega $$
Now$$,$$ the wire is bent such that each side has a resistance $$4\Omega ,$$ (since the resistance is divided uniformly).

Now from the diagram, we can see that between two vertices$$.$$ there is an arrangement of two $$4\Omega $$ resistors in series connected in parallel with another $$4\Omega $$ resistor$$.$$
The net resistance becomes$$:-$$ $$\dfrac{{8 \times 4}}{{8 + 4}} = \dfrac{8}{3}\Omega $$
Hence,
option $$(B)$$ is correct answer.
Question 2
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Current l in the network shown in figure is :-

A
16 A

B
3 A

C
19 A

D
12 A

Solution
Question 3
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In the situation shown, the currents through $$3\Omega$$ and $$2\Omega$$ resistances are in the ratio

A
$$3:2$$

B
$$7:4$$

C
$$4:3$$

D
$$3:1$$

Solution
Question 4
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Kirchhoff's junction law is equivalent to

A
conservation of energy

B
conservation of charge

C
conservation of electric potential

D
conservation of electric flux

Solution
Question 5
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Equivalent resistance between A and B is.

A
3 $$\Omega $$

B
6 $$\Omega $$

C
1.5 $$\Omega $$

D
4.5 $$\Omega $$

Solution
Question 6
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In the given circuit diagram , the currents , $${ I }_{ 1 }=-0.3\quad A,{ I }_{ 4 }=0.8\quad A,and\quad { I }_{ 5 }=0.4\quad A,$$ are flowing as shown . the currents $${ I }_{ 2 }$$,$${ I }_{ 3 }$$

A
0.4 A, 1.1 A,0.4 A

B
1.1 A, 0.4 A, 0.4 A

C
1.1 A, -0.4 A, 0.4 A

D
-0.4 A, 0.4 A , 1.1 A

Solution
Question 7
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What is the minimum resistance which can be made using five resistors each of $$\dfrac{1}{5} \Omega$$?

A
$$\dfrac{1}{5}\Omega$$

B
$$\dfrac{1}{25}\Omega$$

C
$$\dfrac{1}{10}\Omega$$

D
$$\dfrac{1}{50} \Omega$$

Solution

For minimum resistance resistors should be connected in parallel combination.
Suppose value of one resistance is $$R$$.
$$R = \dfrac{1}{5} \Omega$$
Equivalent resistance of $$5$$ resistance-
$$\dfrac{1}{R_{eq}} = \dfrac{1}{R}+\dfrac{1}{R}+\dfrac{1}{R}+\dfrac{1}{R}+\dfrac{1}{R}$$

$$\Rightarrow \dfrac{1}{R_{eq}} = \dfrac{5}{R}$$

$$\Rightarrow {R_{eq}} = \dfrac{R}{5}$$

put the value of $$R$$-

$$\Rightarrow {R_{eq}} = \dfrac{1}{5 \times 5}$$

$$\Rightarrow {R_{eq}} = \dfrac{1}{25} \Omega$$
Question 8
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A particular ohmmeter uses a battery to provide a potential difference across an unknown resistance whose value resistance is to be measured. The meter measures the resulting current through this resistor and is calibrated to read out corresponding value of resistance. Suppose that this ohmmeter is used to measure he resistance of a typical incandescent tungsten-filament light bulb. The value of the resistance of the light bulb will be:

A
less then when the bulb will be in use in a 120 volt circuit

B
more then when the bulb will be in use in a 120 volt circuit

C
the same as then when the bulb will be in use in a 120 volt circuit

D
more information when needed to determine whether it's A,B and C
Question 9
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A potential gradient is created in the wire by standard cell for the comparision of emf's of two cells in a potentiometer experiment. Which possibility of the following will cause failure of the experiment.

A
the emf of the standard cell is higher than that of the other cells.

B
the diameter of the wires is equal and similar,

C
3) the number of wires is ten.

D
the emf of the standard cell is smaller than those of both the cells.

Solution
Question 10
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The magnitude and direction of current I (in A) indicated in the following circuit is

A
14 $$\rightarrow $$

B
8 $$\rightarrow $$

C
$$\leftarrow $$ 4

D
$$\leftarrow $$ 6

Solution