Electricity Test

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Electricity Test - 65

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Weekly Quiz Competition

Question 1
1 / -0

Equivalence Resistance?

A
2R

B
5R

C
3R

D
7R

Solution
Question 2
1 / -0

An electric kettle has two heating coils. When one of the coils is connected to an AC source, the water in the kettle boils in $$10\ min$$. When the other coil is used the water boils in $$40\ min$$. If both the coils are connected in parallel, the time taken by the same quantity of water to boil will be

A
$$25\ min$$

B
$$15\ min$$

C
$$8\ min$$

D
$$4\ min$$

Solution
Question 3
1 / -0

In the network atom in figure, the equivalent resistance between the point A and B is :-

A
$$3 \ \Omega $$

B
$$2 \ \Omega $$

C
$$4 \ \Omega $$

D
$$1 \ \Omega $$

Solution

Between points A and B , $$R_3$$ is parallel to $$R_4$$ and $$ R_5$$ whereas $$R_4$$ and $$R_5$$ are in series.

We know that equivalent resistance in series is given as,
$$R_{eq}=R_1+R_2$$

Equivalent resistance in parallel is given as,
$$\dfrac{1}{R_{eq}} = \dfrac{1}{R_1}+\dfrac{1}{R_2}$$

Since $$R_4$$ and $$R_5$$ are in series, $$R_{45} = 2+4 = 6 \ \Omega$$

Since, $$R_{45}$$ and $$R_3$$ are in parallel,
$$\dfrac{1}{R_{eq}}=\dfrac{1}{3}+\dfrac{1}{6}=\dfrac{2+1}{6}=\dfrac{3}{6}$$

$$R_{eq}=2 \ \Omega $$
Question 4
1 / -0

If two resistances $${R_1} = \left( {10.0 \pm 0.1} \right)\Omega \;and\;{R_2} = \left( {20.0 \pm 0.1} \right)\Omega \;are\;connected$$ in series, then the maximum percentage error in its equivalent resistance will be

A
1/5%

B
2/3%

C
2%

D
4%

Solution

Given,
$$R_1=(10\pm0.1)\Omega$$
$$R_2=(20\pm0.1)\Omega$$
In series combination,
$$R_{eq}=R_1+R_2$$
$$R_{eq}=(10\pm0.1)+(20\pm0.1)=10+20+(\pm0.1)+(0.1)$$
$$R_{eq}=(30\pm0.2)\Omega$$
The maximum percentage error
$$\dfrac{0.2}{30}\times 100=\dfrac{2}{3}$$%
The correct option is B.
Question 5
1 / -0

Two copper wires are of same length one of the twice as thick as the other. Then the resistance of the two wires are in the ratio of :

A
$$1:16$$

B
$$1:8$$

C
$$1:4$$

D
$$1:2$$

Solution
Question 6
1 / -0

Power dissipated across the $$8\Omega$$ resistor in the circuit shown here is $$2W$$. The power dissipated in watt units across the $$3\Omega$$ resistor is

A
$$2$$

B
$$1$$

C
$$0.5$$

D
$$3$$

Solution
Question 7
1 / -0

$$P. Q$$ and $$R$$ are three resistances. When $$P, Q$$ and $$R$$ are connected in parallel, their total resistance is $$3 \Omega.$$ When $$P$$ and $$Q$$ are connected in parallel their total resistance is $$10/ 3\ \Omega.$$ When $$P$$ and $$R$$ is connected in series, their total resistance is $$15\ \Omega.$$ Find the correct value for $$P, Q$$ and $$R.$$

A
$$P \rightarrow 5 \Omega ; Q \rightarrow 30 \Omega ; R \rightarrow 10 \Omega$$

B
$$P \rightarrow 8 \Omega ; Q \rightarrow 10 \Omega ; R \rightarrow 7 \Omega$$

C
$$P \rightarrow 5 \Omega ; Q \rightarrow 10 \Omega ; R \rightarrow 10 \Omega$$

D
$$P \rightarrow 5 \Omega ; Q \rightarrow 10 \Omega ; R \rightarrow 30 \Omega$$
Question 8
1 / -0

The equivalent resistance of fig shown between 'a' and 'b' is

A
$$\dfrac {2r} {8}$$

B
$$\dfrac {5r} {8}$$

C
$$\dfrac {r} {8}$$

D
$$\dfrac {3r} {8}$$

Solution

$$\therefore$$ Option $$B$$ is correct.
Question 9
1 / -0

Find a TRUE statement

A
Ohm's law is applicable to all conductors of electricity

B
The resistance of an incandescent lamp is lesser when the lamp is switched on

C
Specific resistance of a wire depends upon its dimensions

D
The resistance of carbon decreases with an increase in temperature

Solution

Carbon is an insulator and has a negative temperature co-efficient. Hence, its resistance decreases with an increase in temperature.
Question 10
1 / -0

A wire of resistance 'R' is bent into a circular ring of radius r. Equivalent resistance between two points 'x' and 'y' on its circumference, when angle XOT is A, can be given by

A
$$\dfrac { Ra }{ { 4\pi }^{ 2 } } \left( 2\pi -a \right) $$

B
$$\dfrac { R }{ { 2\pi } } \left( 2\pi -a \right) $$

C
$$R\left( 2\pi -a \right) $$

D
$$\dfrac { 4\pi }{ { Ra } } \left( 2\pi -a \right) $$

Solution