Electrostatic Potential and Capacitance Test

Result

Electrostatic Potential and Capacitance Test - 83

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Question 1
1 / -0

If electric potential of a body is zero, than

A
Charge on this must be zero

B
Charge on this may be positive

C
Charge on this may be negative

D
Both $$(B)$$ & $$(C)$$

Solution
Question 2
1 / -0

In the figure shown $$ a+3 \mu c $$ charge and $$ a-2 \mu c $$ charge are placed on the x-axis.in which of the regions on the x-axis is a point where the electrical potential is zero.

A
Region II only

B
Region III only

C
Region II and III

D
Region I, II and III

Solution
Question 3
1 / -0

In the given network of capacitors, the equivalent capacitance between point A and B is

A
$$\frac{6}{5} C$$

B
2 C

C
$$\frac{9}{7} C$$

D
$$\frac{11}{5} C$$

Solution
Question 4
1 / -0

In the given circult, the potenital difference between $$A$$ and $$B$$ is 18V and charge on $$2\,\mu F$$ capacitor is $$24 \, \mu c$$. The value of C is

A
$$1 \,\mu F$$

B
$$2 \,\mu F$$

C
$$3 \,\mu F$$

D
$$4 \,\mu F$$

Solution
Question 5
1 / -0

An air capacitor is connected to a battery of emf V. A dielectric medium of dielectric constant K is introduced between the plates of this capacitor, with the battery still connected. The final charge on the capacitor plates relative to the previous charge

A
is less

B
is more

C
is the same

D
may be more or less depending upon the dielectric constant of the medium

Solution

REF.Image
Initially $$Q = CV$$
$$= \frac{A\varepsilon _{0}}{d}V$$
$$(k=1)$$
But when dielectric
is inserted
$$Q^{1}=K\frac{A\varepsilon _{0}}{d}V$$
$$ k > 1$$
so
$$Q^{1}> Q$$
(B) option is correct.
Question 6
1 / -0

Find the ratio of the equivalent capacitance of the two combination between A and B shown in the figure (a) and (b)

A
$$ \dfrac {4}{3} $$

B
$$ \dfrac {4}{7} $$

C
$$ 1 $$

D
$$ \dfrac {16}{9} $$

Solution
Question 7
1 / -0

Four capacitors of capacitance C,2C, 3C & 4C respectively are connected as shown in figure.Battery is ideal and all the connected wires have no resistance capacitance or inductance.Initially the switch S is open.If at t=0 switch S is closed.
The charge flown through connector AB after switch is closed is.

A
CE

B
CE/2

C
CE/5

D
CE/3

Solution
Question 8
1 / -0

The potential in certain region is given as $$V = 2x^2$$, then the charge density of that region is

A
$$-\dfrac{4x}{\varepsilon _0}$$

B
$$-\dfrac{4}{\varepsilon _0}$$

C
$$-4 \varepsilon_0$$

D
$$-2 \varepsilon_0$$

Solution

By Gauss's law, $$\nabla^2V=-\frac{\rho}{\varepsilon_0}$$
So, $$\frac{\partial^2V}{\partial x^2}=-\frac{\rho}{\varepsilon_0} ...(1)$$
Give, $$V=2x^2$$
or $$\frac{\partial V}{\partial x}=4x$$
or $$\frac{\partial^2V}{\partial x^2}=4$$
Now from (1), $$\rho=-4\varepsilon_0$$
Question 9
1 / -0

Equivalent capacitance of given grouping across $$AB$$

A
$$C$$

B
$$C(\sqrt{2}-1)$$

C
$$C(\sqrt{3}-1)$$

D
$$2 C$$

Solution
Question 10
1 / -0

The equivalent capacitance in the circuit between $$A$$ and $$B$$ will be

A
$$\dfrac{1}{3} \,\mu F$$

B
$$ 3 \,\mu F$$

C
$$2 \,\mu F$$

D
$$ 1\,\mu F$$