Electrostatic Potential and Capacitance Test

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Electrostatic Potential and Capacitance Test - 80

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Weekly Quiz Competition

Question 1
1 / -0

In the given figure, each capacitor is of capacitance $$1 \mu F$$.Calculate the equivalen capacitance between A and B.

A
$$5\mu f$$

B
$$2\mu f$$

C
$$10\mu f$$

D
$$15\mu f$$

Solution
Question 2
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An infinite number of charges each equal to Q are placed along the x-axis at x=1,x=2,x=4,x=8,.......... and so on.Find the potential and electric filed at the point x=0 , due to this set of charges:

A
$$\dfrac{Q}{2 \pi \varepsilon_0},\dfrac{Q}{3 \pi \varepsilon_0}$$

B
$$\dfrac{Q}{10 \pi \varepsilon_0},\dfrac{Q}{3 \pi \varepsilon_0}$$

C
$$\dfrac{5Q}{ \pi \varepsilon_0},\dfrac{Q}{3 \pi \varepsilon_0}$$

D
$$\dfrac{10Q}{2 \pi \varepsilon_0},\dfrac{Q}{3 \pi \varepsilon_0}$$

Solution
Question 3
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The electric potential in a certain region is expressed by $$V = 6x-8xy^2-8y + 6yz - 4z^2$$ volts. The magnitude of the force acting on a charge of $$2C$$ sityuated at the origin wil be:-

A
$$2N$$

B
$$6N$$

C
$$8N$$

D
$$20N$$

Solution
Question 4
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Two parallel plates have equal and opposite charge. When the space between them is evacuated, the electric field between the plates is $$2\times\ 10^5\ V/m$$. When the space is filled with dielectric, the electric field becomes $$1\times\ 10^5\ V/m$$. The dielectric constant of a dielectric material is:

A
$$1/2$$

B
$$1$$

C
$$2$$

D
$$3$$

Solution
Question 5
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The resultant capacity between point $$A$$ and point $$B$$ in the following circuit will be:

A
$$C$$

B
$$\dfrac{C}{2}$$

C
$$2C$$

D
$$3C$$

Solution
Question 6
1 / -0

Four condensers are connected as shown in the figure. The effective capacity in $$\mu F$$ between the points $$A$$ and $$B$$ are :

A
$$28 \mu F$$

B
$$4 \mu F$$

C
$$5 \mu F$$

D
$$18 \mu F$$

Solution
Question 7
1 / -0

Fig. shows a network of four capacitors. Determine the equivalent capacitance between points $$A$$ and $$B$$. If a $$10V$$ battery is connected between $$A$$ and $$B$$, how much total charge will be stored on the capacitors ?

A
$$60\ mu F, 6\ mu C$$

B
$$6\ mu F, 60\ mu C$$

C
$$16\ mu F, 6\ mu C$$

D
$$16\ mu F, 60\ mu C$$
Question 8
1 / -0

In the given circuit, if potential difference between points $$A$$ and $$B$$ is $$4V$$, then, resistance $$X$$ is:-

A
$$5 \Omega$$

B
$$10 \Omega$$

C
$$15 \Omega$$

D
$$20 \Omega$$

Solution
Question 9
1 / -0

The potential difference between points $$A$$ and $$D$$ in the given circuit is:-

A
$$\dfrac{2}{3}V$$

B
$$\dfrac{8}{9}V$$

C
$$\dfrac{4}{3}V$$

D
$$2V$$

Solution

Hint: The potential drop on parallel connection is same.

Step 1: Equivalent resistance through ADC,
The equivalent resistance in the series connection is defined as,
$$R=R_1+R_2+R_3$$
$$R=5\Omega+5\Omega+5\Omega$$
$$R=15\Omega$$

Step 2: Finding the current through ADC,
As the potential drop in the parallel connection, therefore the potential drop across $$15\Omega$$ is same.
According to Ohm's law,
$$V=IR$$
$$I=\dfrac{V}{R}$$
$$I=\dfrac{2}{15}$$

Step 3: Finding the potential drop.
Using the Ohm's law, the potential drop across AD is,
$$V=IR$$
$$V=\dfrac{2}{15}\times 5$$
$$V=\dfrac{2}{3}$$
Question 10
1 / -0

Two condensers of capacities $$C$$ farad and $$2C$$ farad are connected in parallel and then connected in series with a third condenser of capacity $$3C$$ farad. The combination is charged with $$V$$ volt. The charge (in coulomb) on condenser of capacity $$C$$ farad is:

A
$$\dfrac{3CV}{2}$$

B
$$2CV$$

C
$$\dfrac{CV}{2}$$

D
$$CV$$

Solution

$$Q = \dfrac{3C}{2}V$$
$$\dfrac{Q_1}{Q_2} = \dfrac{C}{2C} = \dfrac{1}{2}$$
$$\dfrac{Q_1}{Q_1 + Q_2} = \dfrac{1}{1+2} = \dfrac{1}{3}$$
$$\dfrac{Q_1}{\dfrac{3CV}{2}} = \dfrac{1}{3}$$
$$R_2 = \dfrac{CV}{2}$$