Electrostatic Potential and Capacitance Test

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Electrostatic Potential and Capacitance Test - 76

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Weekly Quiz Competition

Question 1
1 / -0

Find the equivalent capacitance between A and B in the circuit shown below. If the A and B connected across a $$12 V$$, find the electrostatic potential energy of the system. (the capacitance of each capacitor is $$100 \mu F$$)

A
$$225 \mu F, 9 mJ$$

B
$$125 \mu F, 9 mJ$$

C
$$125 \mu F, 19 mJ$$

D
$$225 \mu F, 19 mJ$$

Solution
Question 2
1 / -0

The variation of potential with distance $$R$$ from a fixed point is as shown below. A charge $$q$$ is put at $$R=3\ m$$ and released. The charge will

A
Move away from origin

B
Move towards the origin

C
Not move

D
Trace a circular path

Solution
Question 3
1 / -0

The electric potential at a point in free space due to a charge $$Q$$ coulomb is $$Q\times {10}^{11}V$$. The electric field at that point is

A
$$4\pi { \varepsilon }_{ 0 }Q\times { 10 }^{ 22 }V/m$$

B
$$127\pi { \varepsilon }_{ 0 }Q\times { 10 }^{ 20 }V/m$$

C
$$4\pi { \varepsilon }_{ 0 }Q\times { 10 }^{ 20 }V/m$$

D
$$12\pi { \varepsilon }_{ 0 }Q\times { 10 }^{ 22 }V/m$$

Solution

$$V=Q\times 10^{11}$$
$$E=?$$
$$E=\dfrac{V}{r}=\frac{Q}{4\pi \varepsilon_0 r^2}$$
$$V=\dfrac{Q}{4\pi \varepsilon_0 r}=Q\times 10^{11}$$
$$r=\dfrac{Q}{4\pi \varepsilon_0\times Q\times 10^{11}}$$
$$r=\dfrac{1}{4\pi \varepsilon_0\times 10^{11}}$$
$$E=\dfrac{V}{r}=\dfrac{Q\times 10^{11}}{\dfrac{1}{4\pi \varepsilon_0\times 10^{11}}}=4\pi \varepsilon_0Q\times 10^{22} V/m$$
Question 4
1 / -0

The distance between electric charges $$1\mu C$$ and $$3\mu C$$ is $$8m$$. What is the electric potential at a point on the line joining them where the electric field is zero? ($$k=9\times {10}^{9}$$ SI)

A
$$9\times {10}^{2}$$

B
$$9\times {10}^{3}$$

C
$$9\times {10}^{4}$$

D
$$9\times {10}^{5}$$

Solution
Question 5
1 / -0

A number of capacitors, each of capacitance $$1\mu F$$ and each one of which gets punctured if a potential difference just exceeding $$500$$ volt is applied, are provided. Then an arrangement suitable for giving a capacitor of capacitance $$3\mu F$$ across which $$2000$$ volt may be applied requires at least:

A
$$4$$ component capacitors

B
$$12$$ component capacitors

C
$$48$$ component capacitors

D
$$16$$ component capacitors

Solution
Question 6
1 / -0

The equivalent capacitance between the terminals $$X$$ and $$Y$$ in the figure shown will be -

A
$$100 pF $$

B
$$200 pF $$

C
$$300 pF $$

D
$$400 pF $$

Solution

Let two nodes $$a$$, $$b$$ between the terminal $$X$$ and $$Y$$.
Since between the node $$Y$$ and $$b$$ the two capacitors of $$100\;{\rm{pf}}$$ are in parallel, between the node $$a$$ and $$b$$ the capacitor of $$200\;{\rm{pf}}$$ is in series.
The equivalent capacitance between the node $$Y$$ and $$b$$ is given as,
$${C_1} = 100||100$$
$$ = 200\;{\rm{pf}}$$
The equivalent capacitance between the node $$Y$$ and $$a$$ is given as,
$${C_2} = \left[ {\dfrac{{\left( {200 \times 200} \right)}}{{200 + 200}}||100} \right]$$
$$ = 200\;{\rm{pf}}$$
The equivalent capacitance between the node $$Y$$ and $$X$$ is given as,
$$C = \left[ {\dfrac{{\left( {200 \times 200} \right)}}{{200 + 200}}||100} \right]$$
$$ = 200\;{\rm{pf}}$$

Thus, the equivalent capacitance between the terminals $$X$$ and $$Y$$ is $$200\;{\rm{pf}}$$.
Question 7
1 / -0

A dielectric slab of thickness $$d$$ inserted in a parallel plate capacitor whose negative plate is at $$x=0$$ and positive plate is at $$x=3d$$. The slab is equidistant from the plates. The capacitor is given some charge .As $$x$$ goes from $$0$$ to $$3d$$:

A
$$The\ magnitude\ of\ the\ elecrtric\ field\ remains\ the\ same.$$

B
$$The\ direction\ of\ the\ electric\ field\ remains\ the\ same.$$

C
$$The\ electric\ potential\ increases\ continuously.$$

D
$$The\ electric\ potential\ increase\ at\ first\, then\ decreases\ and\ again\ increases.$$

Solution
Question 8
1 / -0

In the connections shown in the adjoining figure, the equivalent capacity between points $$A$$ and $$B$$ will be

A
$$10.8\ \mu F$$

B
$$69\ \mu F$$

C
$$15\ \mu F$$

D
$$10\ \mu F$$

Solution
Question 9
1 / -0

Four condensers are joined as shown in figure. The capacity of each is $$8\ \mu F$$. The equivalent capacity between the points $$A$$ and $$B$$ will be

A
$$16\ \mu F$$

B
$$2\ \mu F$$

C
$$8\ \mu F$$

D
$$32\ \mu F$$

Solution
Question 10
1 / -0

Five capacitors of $$10\mu F$$ capacity each are connected to a DC potential of $$100V$$ as shown in figure. The equivalent capacity between the points A and B will be

A
$$40\mu F$$

B
$$20\mu F$$

C
$$30\mu F$$

D
$$10\mu F$$

Solution