Electrostatic Potential and Capacitance Test

Result

Electrostatic Potential and Capacitance Test - 85

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Weekly Quiz Competition

Question 1
1 / -0

Four metallic plates are arranged as shown in the figure. If the distance between each plate then capacitance of the given system between points A and B is (Given d<<A)

A
$$\frac{\varepsilon _oA}{d}$$

B
$$\frac{2\varepsilon _0A}{d}$$

C
$$\frac{3 \varepsilon _o A}{d}$$

D
$$\frac{4 \varepsilon _o A}{d}$$
Question 2
1 / -0

Condenser A has a capacity of 15 $$\mu F$$ when it is filled with a medium of dielectric constant 15. Another condenser B has a capacity 1 $$\mu F$$ with air between the plates. Both are charged separately by a battery of 100V. After charging, both are connected in parallel without the battery and the dielectric material being removed. The common potential now is

A
400 V

B
800 V

C
1200 V

D
1600 V

Solution
Question 3
1 / -0

Two parallel plate capacitors X and Y have the same area of plates and same separation between them. X has air between the plates while Y contains a dielectric medium of $$ \varepsilon _r=4$$.

A
Calculate capacitance of each capacitor if equivalent capacitance of the combination is $$4 \mu F$$.

B
Calculate the potential difference between the plates of X and Y.

C
Estimate the ratio of electrostatic energy stored in X and Y.

D
None of these
Question 4
1 / -0

In a parallel-plate capacitor with plate area $$A$$ and charge $$Q$$ the force on one plate because of the charge on the other is equal to.

A
$$\dfrac{Q^2}{\varepsilon_0 A^2}$$

B
$$\dfrac{Q^2}{2\varepsilon_0 A^2}$$

C
$$\dfrac{Q^2}{\varepsilon_0 A}$$

D
$$\dfrac{Q^2}{2\varepsilon_0 A}$$

Solution
Question 5
1 / -0

Determine equivalent capacitance between A and B Each capacitance is of $$1$$ F.

A
$$1$$ F

B
$$2$$ F

C
$$3$$ F

D
$$4$$ F

Solution
Question 6
1 / -0

The resultant capacitance between points A and B in the adjoining figure

A
$$ 1 \mu F $$

B
$$ 1.5 \mu F $$

C
$$ 2 \mu F $$

D
$$ 3 \mu F $$
Question 7
1 / -0

Find equivalent capacitance of the given circuit.

A
$$\frac { c } { 5 }$$

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

C
$$\frac { 3 c } { 5 }$$

D
$$\frac { 3 c } { 10 }$$

Solution
Question 8
1 / -0

Find a capacitance

A
$$\dfrac{2kA\varepsilon_0}{d}$$

B
$$\dfrac{2kA\varepsilon_0}{(k+1)d}$$

C
$$\dfrac{(k+1)A\varepsilon_0}{2d}$$

D
$$\dfrac{2kA\varepsilon_0}{(k^2+1)d}$$

Solution
Question 9
1 / -0

Consider an infinite matrix of capacitors as shown in the figure.
The effective capacitance between point $$A$$ and $$B$$ will be

A
$$C$$

B
$$2C$$

C
$$\infty$$

D
Can't be determined

Solution
Question 10
1 / -0

In the given circuit, find the potential difference across the 6$$\mu \mathrm { F }$$ capacitor in steady state.

A
$$4 V$$

B
$$2 V$$

C
$$6 V$$

D
$$8 V$$

Solution

$$\begin{array}{l} At\, \, steady\, \, state\, \, all\, \, the\, \, capacitor\, \, acts\, \, as\, \, the\, \, open\, \, circuit. \\ find\, \, the\, \, difference\, \, { V_{ CD } } \\ resis\tan ce\, \, across\, \, CD=\left( { 1.5+1.5 } \right) \parallel \left( { 1.5+1.5 } \right) +1.5=3\, \Omega \\ { V_{ CD } }=8\left( { \frac { 3 }{ 4 } } \right) =6\, V \\ potential\, \, difference\, \, across\, \, 6\mu F=6\left( { \frac { 3 }{ 9 } } \right) =2V \end{array}$$
Hence,
option $$(B)$$ is correct answer.