Electrostatic Potential and Capacitance Test

Result

Electrostatic Potential and Capacitance Test - 79

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Weekly Quiz Competition

Question 1
1 / -0

Plates of area A are arranged as shown. The distance between each plate is d,the net capacitance is

A
$$\dfrac{\varepsilon_oA}{d}$$

B
$$\dfrac{7 \varepsilon_oA}{d}$$

C
$$\dfrac{ 6\varepsilon_oA}{d}$$

D
$$\dfrac{ 5 \varepsilon_oA}{d}$$

Solution
Question 2
1 / -0

Find the charge on each capacitor in the given network. Each capacitor has a capacitance of $$6\mu F$$.

A
$$1.44\times 10^{-3}C$$ on $$C_{4} : 3.6\times 10^{-4}C$$ on each of remaining.

B
$$1.44\times 10^{-3}C$$ on $$C_{4} : 1.6\times 10^{-4}C$$ on each of remaining.

C
$$2.44\times 10^{-3}C$$ on $$C_{4} : 3.6\times 10^{-4}C$$ on each of remaining.

D
$$5.44\times 10^{-3}C$$ on $$C_{4} : 4.6\times 10^{-4}C$$ on each of remaining.

Solution
Question 3
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Charge $$5 \mu\ C$$,$$-2 \mu\ C$$,and $$-9 \mu\ C$$ are placed at the comers A,B,C and D of a square ABCD of side $$2m$$. The electric potential at the center of the square is:

A
$$-27KV$$

B
$$ -27\sqrt { 2 }$$

C
$$-90KV$$

D
$$zero$$

Solution
Question 4
1 / -0

In a given circuit diagram charge on capacitor 6 $$\mu F$$ is 2 $$\mu C$$. The charge on capacitor of capacity 4 $$\mu F$$ is :

A
2 $$\mu C$$

B
4 $$\mu C$$

C
6 $$\mu C$$

D
8 $$\mu C$$

Solution
Question 5
1 / -0

Four capacitors of each of capacity $$3 \mu F $$ are connected as shown in the adjoining figure. The ratio of equivalent capacitance between $$A$$ and $$B$$ and between $$A$$ and $$C$$ will be :

A
$$4:3$$

B
$$3:4$$

C
$$2:3$$

D
$$3:2$$

Solution

Equivalent capacitance between A and B

One capacitor of $$3\;{\rm{\mu F}}$$ is parallel to three capacitor each of $$3\;{\rm{\mu F}}$$which are in series to each other.

Equivalent capacitance of three capacitors

$$\frac{1}{C} = \frac{1}{3} + \frac{1}{3} + \frac{1}{3}$$

$$C = 1\;{\rm{\mu F}}$$

Now Let equivalent capacitance between A and B be $${C_1}$$.

$${C_1} = 1 + 3$$

$${C_1} = 4\;{\rm{\mu F}}$$

Now equivalent capacitance between A and C

Here two capacitors are in series to each other and parallel to another set of two capacitors in series.

Equivalent capacitance of two capacitors in series

$$\frac{1}{C} = \frac{1}{3} + \frac{1}{3}$$

$$C = 1.5\;\Omega $$

Let equivalent capacitance between A and C is $${C_2}$$.

$${C_2} = 1.5 + 1.5$$

$${C_2} = 3\;{\rm{\mu F}}$$

Ratio of capacitance

$$r = \frac{{{C_1}}}{{{C_2}}}$$

$$r = \frac{4}{3}$$
Question 6
1 / -0

The equivalent capacitance between the points A and in the given diagram is:

A
$$8\mu F$$

B
$$6\mu F$$

C
$$\dfrac{8}{3} \mu F$$

D
$$\dfrac{3}{8} \mu F$$

Solution

$$\dfrac { 1 }{ { C }_{ eqv } } =\dfrac { 1 }{ 2 } +\dfrac { 1 }{ 2 } +\dfrac { 1 }{ 2 } +\dfrac { 1 }{ 2 } =\dfrac { 2 }{ 16 } $$

$${ C }_{ eqv }=\dfrac { 16 }{ 2 } =8\mu F$$
Question 7
1 / -0

Two parallel plate capacitors are connected in series. Each capacitor has a plate area A and a separation d between the plates. The dielectric constant of the medium between their plates are 2 and 4 . The separation between the plates of a single air capacitors of plate area A which effectively replaces the combination is:

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

B
$$\dfrac{3d}{2}$$

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

D
$$\dfrac{8d}{5}$$

Solution
Question 8
1 / -0

A technician has only two capacitors. By using them singly, in series or in parallel, he is able to obtain the capacitances of $$3 \mu F$$, $$4 \mu F$$ ,$$12 \mu F$$ and $$16 \mu F$$. The capacitances of the two capacitrs are:

A
$$4 \mu F$$ and $$12 \mu F$$

B
$$4 \mu F$$ and $$16 \mu F$$

C
$$6 \mu F$$ and $$10 \mu F$$

D
$$7 \mu F$$ and $$9 \mu F$$

Solution
Question 9
1 / -0

The equivalent capacitance between the points $$A$$ and $$B$$ in the given diagram is:

A
$$8\mu F$$

B
$$6\mu F$$

C
$$\frac{8}{3}\mu F$$

D
$$\frac{3}{8}\mu F$$

Solution
Question 10
1 / -0

A non conducting semicircular disc (as shown in figure) has a uniform surface charge density $$\sigma $$. The electric potential at the centre of the disc:-

A
$$\dfrac{\sigma \ \iota n(b/a)}{2\pi \ \varepsilon _{0}\ (b-a)}$$

B
$$\dfrac{\sigma (b-a)}{2\ \varepsilon _{0}}$$

C
$$\dfrac{\sigma (b-a)}{4\ \varepsilon _{0}}$$

D
$$\dfrac{\sigma (b-a)}{4\pi \ \varepsilon _{0}}$$

Solution