Electrostatic Potential and Capacitance Test

Result

Electrostatic Potential and Capacitance Test - 64

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Weekly Quiz Competition

Question 1
1 / -0

The circuit was in the shown state for a long time. Now if the switch S is closed then the met net charge that flows through the switch S, will be

A
$$\frac{400}{3}$$ $$\mu C$$

B
100 $$\mu C$$

C
$$\frac{100}{3}$$ $$\mu C$$

D
50 $$\mu C$$

Solution
Question 2
1 / -0

If a thin metal foil of the same area is placed between the two plates of a parallel plate capacitor capacitance C, then new capacitance will be

A
C

B
2C

C
3C

D
4C

Solution

We have,

$$C=\dfrac{\epsilon_0 A}{d}$$

After placement of plate of equal area in between the two plates, we have two capacitors in series.

Value of each capacitor,

$$C_1=\dfrac{\epsilon_0 A}{d/2}$$

$$C_1=\dfrac{2\epsilon_0 A}{d}=2C$$

Equivalent capacitance, $$C_{eq}=\dfrac{2C \times 2C}{2C+2C}$$

$$\implies C_{eq}=C$$
Question 3
1 / -0

As shown in the figure, two identical capacitors are connected to a battery of V voltin parallel. When capacitors are fully charged, their stored energy is $$U_1$$. If the key $$K$$ is opened and a material of dielectric constant K=3 is inserted in each capacitor, their stored energy is now $$U_2 \cdot \frac{U_1}{U_2}$$ will be

A
$$\frac{5}{3}$$

B
$$\frac{3}{5}$$

C
$$3$$

D
$$\frac{1}{3}$$

Solution
Question 4
1 / -0

A parallel plate capacitor of capacitance,$$C$$ (without dielectrics) is filled by dielectric slabs as shown in figure.Then the new capacitance of the capacitor is

A
$$39C$$

B
$$4C$$

C
$$34C$$

D
$$3C$$

Solution

Ref. Image I
Ref. Image II $$C_1 = \dfrac{K \varepsilon_0 A}{\dfrac{d}{2}}$$
$$= 2 \times 6 \times \dfrac{\varepsilon_0 A}{d}$$
$$= 12C$$
$$C_2 = \dfrac{K_2 \varepsilon_0 \dfrac{A}{2}}{\dfrac{d}{2}} = 2C$$
$$C_3 = \dfrac{K_3 \varepsilon_0 \dfrac{A}{2}}{\dfrac{d}{2}} = 4 \dfrac{\varepsilon_0 A}{d} = 4 C$$
$$C_{eq} = C_2 + C_3$$ Ref. image III
$$= 4C + 2C$$
$$= 6C$$
$$C_{eq} = \dfrac{12C \times 6C}{12 C + 6C} = \dfrac{72 C^2}{18 C}$$
$$C_{eq} = 4C$$
Question 5
1 / -0

Six equal capacitors each of capacitance $$C$$ are connected as shown in the figure. The equivalent capacitance between $$A$$ and $$B$$ is:

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

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

C
$$C$$

D
None of these
Question 6
1 / -0

Four metal conductors having different shapes are mounted on insulating stands and charged.The one which is best suited to retain the charges for a longer time is.

A
A sphere

B
Cylindrical

C
Pear

D
Lightning conductor.

Solution
Question 7
1 / -0

The equivalent capacitance between the points P and Q in the following arrangement of capacitor is

A
$$ 4 \mu F $$

B
$$ 2 \mu F $$

C
$$ 4/3 \mu F $$

D
$$ 12 \mu F $$
Question 8
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
Question 9
1 / -0

A capacitive network of complex combination is shown in the figure.The energy stored in $$ 4 \mu F $$ capacitor is.

A
$$ 200 \mu J $$

B
$$ 400 \mu J $$

C
$$ 100 \mu J $$

D
$$ 600 \mu J $$
Question 10
1 / -0

The potential difference between the plates of a parallel plate capacitor is $$3.2\times 10^{4}V$$. A charge particle of mass $$4.0\times 10^{-13}kg$$ and charge $$2.4\times 10^{-18}C$$ is inserted between them. What should be the distance between the plates such that the particle remains stationary?

A
$$1.8\ cm$$

B
$$2.0\ cm$$

C
$$2.4\ cm$$

D
$$2.8\ cm$$