Electricity Test

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Electricity Test - 37

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Weekly Quiz Competition

Question 1
1 / -0

The resistors of resistances $$2 \Omega, 4 \Omega, 5 \Omega$$ are connected in parallel. The total resistance of the combination will be :

A
$$\displaystyle \frac{29}{10} \Omega$$

B
$$\displaystyle \frac{19}{20} \Omega$$

C
$$\displaystyle \frac{10}{20} \Omega$$

D
$$\displaystyle \frac{20}{19} \Omega$$

Solution

According to parallel combination.
$$\displaystyle \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}+\frac{1}{R_3}$$
$$=\displaystyle \frac{1}{2} + \frac{1}{4} + \frac{1}{5}$$
$$=0.5 + 0.25 + 0.2$$
$$=0.95 \Omega$$
$$\therefore R_{eq} \displaystyle =\frac{1}{0.95} =\frac{20}{19} \Omega$$
Question 2
1 / -0

Which one of the following is different from the others?

A
Joule

B
Kilowatt hour

C
Erg

D
Watt

Solution
Question 3
1 / -0

What is one unit of household electrical energy in J?

A
$$1000\ J$$

B
$$3600\ J$$

C
$$0.6 \times 10^3 J$$

D
$$3.6 \times 10^6 J$$

Solution

One unit of household is $$1\ kwh$$
$$kwh\ =$$ kilo watt hour
$$1\ \text{unit}$$$$= 1\ kWh$$
$$\Rightarrow 1\ \text{unit} =10^3 W \times 3600\ s$$
$$\Rightarrow 1\ \text{unit} = 3.6 \times 10^6 J $$
Question 4
1 / -0

Four wires are made of same material and have radii (r) and length (l) as given. The wire with least resistance is have

A
$$r=2 mm,\ l=200 cm$$

B
$$r=4 mm,\ l=400 cm$$

C
$$r=1 mm,\ l=100 cm$$

D
$$r=6 mm,\ l=300 cm$$

Solution
Question 5
1 / -0

In the network given below, the current flowing through the resistance $$2 R$$ is

A
$$\dfrac { E }{ R } $$

B
$$\dfrac { E }{ 7R } $$

C
$$\dfrac { 2E }{ 7R } $$

D
$$\dfrac { 2E }{ R } $$
Solution
The combination of given resistors is a series combination of $$R$$ and parallel combination of $$4R, 2R$$.
Resultant resistance of $$4R$$ and $$2R$$:
$$\dfrac{1}{R_p}=\dfrac{1}{4R}+\dfrac{1}{2R}$$
$$\Rightarrow R_p=\dfrac{(4R)(2R)}{2R+4R}=\dfrac{8R^2}{6R}=\dfrac{4R}{3}$$
Resultant resistance of $$R+(4R||2R)$$
$$R_{eq}=R+R_p$$
$$\Rightarrow R_{eq}= R+ \dfrac{4R}{3}= \dfrac{7R}{3}$$

By Ohm's law,
Current supplied by the battery $$I=\dfrac{E}{R_{eq}}=\dfrac{3E}{7R}$$

Voltage across the parallel branch is $$V_p = I \times R_p$$
$$\Rightarrow V_p=\left( \dfrac{3E}{7R} \right) \left(\dfrac{4R}{3}\right)=\dfrac{4E}{7}$$

The voltage $$V_p$$ would be same across $$4R$$ as well as $$2R$$ as they are connected across the same two points.

Hence, current across $$2R$$ is
$$I_{2R} = \dfrac{V_p}{2R} = \dfrac{\left( \dfrac{4E}{7}\right)}{2R}$$

$$I_{2R} = \dfrac{2E}{7R}$$

Option C is correct.
Question 6
1 / -0

The least resistance that can be obtained by combining resistance of $$6 \Omega, 3 \Omega$$ and $$X \Omega$$ is $$1 \Omega$$.
Then $$X$$ is

A
$$3 \Omega$$

B
$$2 \Omega$$

C
$$4 \Omega$$

D
$$6 \Omega$$

Solution

Here, we are given two resistance say
$$R_{1} = 6\Omega$$
$$R_{2} = 3\Omega$$
$$R_{3} = x\Omega$$
Equivalent Resistance (least) $$= 1\Omega$$
We know that equivalent resistance of a combination is minimum when all the resistances are connected in parallel.
So,
$$\dfrac {1}{R_{eq}} = \dfrac {1}{R_{1}} + \dfrac {1}{R_{2}} + \dfrac {1}{R_{2}}$$

$$\Rightarrow \dfrac {1}{1} = \dfrac {1}{6} + \dfrac {1}{3} + \dfrac {1}{x}$$

$$ \Rightarrow \dfrac {1}{x} = 1-\dfrac {1}{6} - \dfrac{1}{3}$$

$$\Rightarrow \dfrac {1}{x} = \dfrac {1}{2}$$

$$\Rightarrow \dfrac {1}{x} = \dfrac {1}{2}$$

$$ \Rightarrow x = 2\Omega$$
Hence value of $$x$$ is $$2\Omega$$, option B is correct.
Question 7
1 / -0

In case of electronic current the charge flows from negatively charged body to the positively charged body. The body which is at higher potential is

A
negatively charged body

B
positively charged body

C
both are at same potential

D
none of these

Solution

By convention a positively charged body is always at a higher potential as compared to negatively charged body . If positive charges like protons or positive ions are free to move they would move from higher potential point to lower potential point.
In case of electronic current the charge flows from negatively charged body to the positively charged body. The body which is at higher potential is positively charged body
Question 8
1 / -0

Energy of the electric current is

A
Thermal

B
Nuclear

C
Electrical

D
Chemical

Solution

$$\textbf{Given:}$$ Different energy forms.
$$\textbf{To find:}$$ Which form of energy is the energy of electric current.
We know electric current flows in a circuit due to potential differences. Electric current flows due to the work done on each charge to move it across the potential difference. The charges contain energy which gives them the capacity to do this work. The nature of this energy is electrical.

So option (C) is correct.
Question 9
1 / -0

A resistance of $$0.01\ \Omega$$ is connected in parallel with a resistance of $$1\ k\Omega$$ The resistance of the combination will be:

A
$$1000\ \Omega$$

B
$$10\ \Omega$$

C
$$1\ \Omega$$

D
$$0.01\ \Omega$$

Solution

initial velocity, $$u = 10\ m/s$$
Resistances,
$$R_1 = 0.01\ \Omega$$
$$R_2 = 1K\ \Omega = 1000\ \Omega$$
for 2 resistances, connected in parallel equivalent resistance, $$R_{eq}$$

$$\dfrac{1}{R_{eq}} = \dfrac{1}{R_1} + \dfrac{1}{R_2} = \dfrac{1}{0.01} + \dfrac{1}{1000}$$

$$\dfrac{1}{R_{eq}} = \dfrac{100000 + 1}{1000}$$

$$R_{eq} = \dfrac{1000}{100001} = 0.009999$$

$$R_{eq} \sim 0.01\ \Omega$$
Question 10
1 / -0

A current of $$3\ A$$ flows through a resistance when it is connected across a 12V source. What should the current be if the resistance is increased by $$4\ \Omega$$ and connected across the same voltage source?

A
$$1.5\ A$$

B
4 A

C
1.6 A

D
24 A

Solution

$$\underline{\text{First Case:}}$$
Voltage $$V_1=12\ V$$
Current $$I=3\ A$$
Resistance = $$R$$
From Ohm's law: $$12=3\times R$$
$$\therefore R=\dfrac{12}{3} = 4\ \Omega$$

$$\underline{\text{Second Case:}}$$
Voltage $$V_2=12\ V$$
Resistance = $$R+4=8\ \Omega$$
From Ohm's law: $$12=I'\times 8$$
$$\therefore I'=\dfrac{12}{8}=1.5\ A$$

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Electricity Test - 37

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Electricity Test - 37

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Question 1

$$\displaystyle \frac{29}{10} \Omega$$

$$\displaystyle \frac{19}{20} \Omega$$

$$\displaystyle \frac{10}{20} \Omega$$

$$\displaystyle \frac{20}{19} \Omega$$

Solution

Question 2

Joule

Kilowatt hour

Erg

Watt

Solution

Question 3

$$1000\ J$$

$$3600\ J$$

$$0.6 \times 10^3 J$$

$$3.6 \times 10^6 J$$

Solution

Question 4

$$r=2 mm,\ l=200 cm$$

$$r=4 mm,\ l=400 cm$$

$$r=1 mm,\ l=100 cm$$

$$r=6 mm,\ l=300 cm$$

Solution

Question 5

$$\dfrac { E }{ R } $$

$$\dfrac { E }{ 7R } $$

$$\dfrac { 2E }{ 7R } $$

$$\dfrac { 2E }{ R } $$

Solution

Question 6

$$3 \Omega$$

$$2 \Omega$$

$$4 \Omega$$

$$6 \Omega$$

Solution

Question 7

negatively charged body

positively charged body

both are at same potential

none of these

Solution

Question 8

Thermal

Nuclear

Electrical

Chemical

Solution

Question 9

$$1000\ \Omega$$

$$10\ \Omega$$

$$1\ \Omega$$

$$0.01\ \Omega$$

Solution

Question 10

$$1.5\ A$$

4 A

1.6 A

24 A

Solution

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