Electricity Test

Result

Electricity Test - 77

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Question 1
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A bulb rated at (100W-200V) is used on a 100 V line. The current in the bulb is

A
1/4 amp

B
4 amp

C
1/2 amp

D
2 amp

Solution

Given,
$$P = 100\ W$$; power of the bulb
$$V = 200\ V$$; voltage rating
So value of resistance-
$$P = \dfrac{V^2}{R}$$
$$\Rightarrow R = \dfrac{V^2}{P}$$

$$\Rightarrow R = \dfrac{200^2}{100}$$

$$\Rightarrow R = 400\ \Omega$$

Now applied voltage changes to $$100\ V$$, so current passing through the resistance-
$$I = \dfrac{V}{R}$$
$$\Rightarrow I = \dfrac{100}{400}$$

$$\Rightarrow I = \dfrac{1}{4} A$$
Question 2
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The rate of change of magnetic field inside a solenoid is constant($$\alpha$$)
. Then the induced electric field inside the solenoid at a distance 'a' from its axis is

A
$$\dfrac { a\alpha }{ 2 } $$

B
$$a\alpha $$

C
Along the axis of solenoid

D
Forming circular loop

Solution
Question 3
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The reading of the ammeter is:

A
$$\dfrac { 1 }{ 8 }\ A$$

B
$$\dfrac { 3 }{ 4 }\ A$$

C
$$\dfrac { 1 }{ 2 } \ A$$

D
$$2\ A$$

Solution
Question 4
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The wires of same dimension but different resistivities $$ \rho_1$$ and $$\rho_2 $$ are connected in parallel. The equivalent resistivity of the combination is

A
$$ \dfrac {\rho_1 + \rho_2}{2} $$

B
$$ 2 (\rho_1 + \rho_2) $$

C
$$ \dfrac {\rho_1 \rho_2}{\rho_1 + \rho_2} $$

D
$$ \sqrt {\rho_1\rho_2} $$

Solution
Question 5
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Meeta connected 4 resistors in parallel. Each has a resistance of $$ 2 \Omega $$. Find the effective resistance .

A
$$8\Omega $$

B
$$4\Omega $$

C
$$0.5\Omega $$

D
$$0.4\Omega $$

Solution
Question 6
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A copper wire of resistance $$R$$ is cut into ten parts of equal length. Two-piece are joined in series and then five such combinations are joined in parallel. The new combination will have resistance.

A
$$R$$

B
$$\frac { R } { 4 }$$

C
$$\frac { R } { 5 }$$

D
$$\frac { R } { 25 }$$

Solution
Question 7
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Most of the times we connect remote speakers to play music in another room along with the built-in speakers. These speakers are connected in parallel with the music system.
At the instant represented in the picture, the voltage across the speakers is $$6.00 V.$$ The resistance of the main speaker is $$ 8 \space \Omega$$ and the remote speaker has resistance $$ 4 \space \Omega$$
The equivalent resistance of the speakers is

A
$$ 12 \space \Omega$$

B
$$ \dfrac{7}{3 }\space \Omega$$

C
$$ \dfrac{8}{3}\space \Omega$$

D
$$ 0.375 \space \Omega$$
Question 8
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Directions For Questions

Consider $$12$$ resistors arranged symmetrically in shape of bi-pyramid $$ABCDEF$$. Here $$ABCD$$ is a square. Point $$E$$, paint $$F$$, and center of square are in the same straight line perpendicular to the plane of square. The resistance of each resistor is $$R$$.

...view full instructions

The effective resistance between $$A$$ and $$B$$ is

A
$$7R/12$$

B
$$5R/7$$

C
$$5R/12$$

D
$$none\ of\ these$$

Solution

Let us remove the resistance between $$A$$ and $$B$$,
then $$E$$ and $$F$$ will be at the same potential, we can draw the remaining as:

$$M$$ is the midpoint of $$DC, M$$ will be at the same pot as $$E$$ and $$F$$.

Now finf $$R_{AB}=5/7R$$.
The resistance which we had removed will be in parallel to it so

$$R_{eq}=\dfrac {R_{AB}R}{R_{AB}+R}=\dfrac {(5/7)RR}{(5/7)R+R}=\dfrac {5}{12}R$$
Question 9
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The equivalent resistance of the circuit across points A and B is equal to

A
$$22.5 \space \Omega$$

B
$$25 \space \Omega$$

C
$$37.5 \space \Omega$$

D
$$75 \space \Omega$$

Solution
Question 10
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A metal wire of resistance $$3\Omega$$ is elongated to make a uniform wire of double its previous length. This new wire is now bent and the ends joined to make a circle. If two points on this circle make an angle $$60^o$$ at the centre, the equivalent resistance between these two points will be?

A
$$\dfrac{12}{5}\Omega$$

B
$$\dfrac{5}{3}\Omega$$

C
$$\dfrac{5}{2}\Omega$$

D
$$\dfrac{7}{2}\Omega$$

Solution

$$R=\dfrac{\rho l^2}{AlD}d=\dfrac{\rho dl^2}{m}$$
$$R\propto l^2$$
$$R=12\Omega$$ (new resistance of wire)
$$R_1=2\Omega$$
$$R_2=10\Omega$$
$$R_{eq}=\dfrac{10\times 2}{10+2}=\dfrac{5}{3}\Omega$$.