Electrostatic Potential and Capacitance Test

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Electrostatic Potential and Capacitance Test - 57

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Weekly Quiz Competition

Question 1
1 / -0

The capacitance of a parallel plate capacitor is $$2.5\mu F$$. When it is half-filled with a dielectric shown in the figure Its capacitance becomes $$5\mu F$$, the dielectric constant of the dielectric is :

A
$$7.5$$

B
$$3.0$$

C
$$0.33$$

D
$$4.0$$

Solution

Let area of each plate be A and spacing between then be d.
Then capacitance of parallel plate capacitor, $$C = \dfrac{\epsilon_0A}{d} = 2.5\mu F$$

When it is half filled with dielectric, capacitance of capacitor filled with air, $$C_1 = \dfrac{\epsilon_0 (A/2)}{d}$$

capacitance of capacitor filled with medium of dielectric constant $$ k$$ is $$C_2 = \dfrac{k\epsilon_0 (A/2)}{d}$$

Since $$C_1$$ and $$C_2$$ are in parallel, equivalent capacitance will be, $$C' = C_1+C_2 = 5\mu F$$

$$\dfrac{\epsilon_0A}{2d} +\dfrac{k\epsilon_0}{2d} = 5$$

$$\dfrac{2.5}{2} +\dfrac{k\times2.5}{2} = 5$$

$$1+k = 4$$

$$k =3$$
Question 2
1 / -0

In the circuit shown in figure $$C=6\mu F$$. The charge stored in the capacitor of capacity $$C$$ is($$Voltage =10V$$):

A
Zero

B
$$90\mu C$$

C
$$40\mu C$$

D
$$60\mu C$$

Solution
Question 3
1 / -0

A parallel plate capacitor with air between the plates has a capacitance of 2pF. The capacitance if the distance between the plates is reduced by half, and the space between them is filled with a substance of dielectric constant 6 is

A
12pF

B
24pF

C
6pF

D
18pF

Solution

We know,

$$C=\dfrac{Ak\varepsilon_0}{d}$$

Given,
For $$k=1,$$
$$C=\dfrac{A\varepsilon_0}{d}=2$$

For k=6, and $$d\rightarrow \dfrac{d}{2}$$

$$C=\dfrac{A\times 6\varepsilon_0}{\dfrac{d}{2}}$$

$$C=\dfrac{12A\varepsilon_0}{d}=12C=24pF$$

Option $$\textbf B$$ is the correct answer
Question 4
1 / -0

A dielectric slab is inserted between the plates of a capacitor is $$Q$$ and the magnitude of the induced charges on each surface of the dielectric is $$Q$$,

A
$$Q^{'}$$ may be larger then $$Q$$

B
$$Q^{'}$$ may be smaller then $$Q$$

C
$$Q^{'}$$ may be equal then $$Q$$

D
None of the above
Question 5
1 / -0

Determine the equivalent capacitance between point $$S$$ and $$V$$, as shown in fig.

A
$$4.8\mu F$$

B
$$2 \mu F$$

C
$$10.8\mu F$$

D
$$18\mu F$$
Question 6
1 / -0

A parallel plate capacitor consists of two circular disc separated by a small distance it is capacitance of see the radius of discus half and separation between disc is doubled a medium of dielectric constant K is introduced between the desk the new capacitance is found to be same as that of the original capacitance C the dielectric constant of medium is

A
$$2$$

B
$$3$$

C
$$8$$

D
$$6$$
Question 7
1 / -0

Six identical square metallic plates are arranged as shown in figure length of each plate is l the capacitance of this arrangement should be

A
$$3\epsilon_0l^2/d$$

B
$$4\epsilon_0l^2/d$$

C
$$3\epsilon_0l^2/2d$$

D
$$2\epsilon_0l^2/d$$
Question 8
1 / -0

Find the equivalent capacitance across A & B

A
$$\dfrac{28}{3} \mu f$$

B
$$\dfrac{15}{2} \mu F$$

C
15 mF

D
none

Solution

The Capacitance $$23\mu f$$ and $$12\mu f,1\mu f$$ and $$1\mu f$$ are connected in paralled so their equivalent capacitance is : $$(23+12)\mu f,(1+1)\mu f$$ respectively i,e
$$35\mu f$$ and $$2\mu f$$
Now the whole circuit is in form of wheatsfftone bridge with :
$$C_{1}=35\mu f,C_{2}=\mu f,C_{3}=10\mu f$$ and $$C_{4}=2\mu f$$
Clearly, $$\dfrac{C_{1}}{C_{2}}=\dfrac{C_{3}}{C_{4}}=5$$
So $$13\mu f$$ capacitor is neglected
Now equivalent capacitance of $$C_{1}$$ and $$C_{2}$$ in series = $$\dfrac{C_{1}C_{2}}{C_{1}+C_{2}}\mu f$$
Equivalent capacitance of $$C_{3} $$ and $$C_{4}$$ in series = $$\dfrac{10\times 2}{10+2}=\dfrac{20}{12}$$$$\mu f$$
Now these two equivalent capacitances are connected in parallel so their equivalent is :
$$C_{eq}=\dfrac{245}{42}+\dfrac{20}{12}=\dfrac{15}{2}\mu f$$
Question 9
1 / -0

A capacitor of capacitance 1 $$\mu F$$ withstands the maximum voltage 6 kV while a capacitor of 2 $$\mu F$$ withstands the maximum voltage 4 kV. What maximum voltage will the system of these two capacitor withstands if they are connected in series?

A
10 kV

B
12 kV

C
8 kV

D
9 kV

Solution
Question 10
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The potential difference between points $$A$$ and $$B$$ in the circuit shown in figure, will be:-

A
$$1 V$$

B
$$2 V$$

C
$$-3 V$$

D
None of these