Electrostatic Potential and Capacitance Test

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Electrostatic Potential and Capacitance Test - 65

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Weekly Quiz Competition

Question 1
1 / -0

Find equivalent capacitance between points $$A$$ and $$B$$

A
$$\dfrac43{ C }$$

B
$$\dfrac34{ C }$$

C
$$\dfrac{10}3{ C }$$

D
$$\dfrac73{ C }$$
Question 2
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The capacity of parallel plate condenser is $$ 12 \mu F $$. What is its new capacity if the separation between the plates is doubled and the area is halved?

A
$$ 1.5 \mu F $$

B
$$ 3 \mu F $$

C
$$ 6 \mu F $$

D
$$ 8 \mu F $$
Question 3
1 / -0

Five conducting parallel plates having area A and separation between them d, are placed as shwon in the figure. plate number 2 and 4 are connected wire and between point A and B , a cell of emf E is connected. the charge flown through the cell is

A
$$ \frac {3}{4} \frac {\varepsilon_0AE}{d} $$

B
$$ \frac {2}{3} \frac {\varepsilon_0AE}{d} $$

C
$$\frac {4 \varepsilon_0AE}{d} $$

D
$$\frac {\varepsilon_0AE}{2d} $$
Question 4
1 / -0

Find equivalent capacitance between A and b of the given circuit.

A
$$ 5 \mu F $$

B
$$ \frac {9}{5} \mu F$$

C
$$ \frac {9}{2} \mu F $$

D
$$ \frac {21}{4} \mu F$$

Solution
Question 5
1 / -0

In the circuit in the figure,in steady state,

A
The charge in $$ 5 \mu F$$ capacitor is $$30 \mu C $$.

B
The charge in $$ 10 \mu F$$ capacitor is $$40 \mu C $$.

C
The charge in $$ 4 \mu F$$ capacitor is $$32 \mu C $$.

D
The current drawn from battery is 1 A.
Question 6
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Two capacitor of capacity $$C_{1}$$ and $$C_{2}$$ are connected in series. The combined capacity $$C$$ is given by

A
$$C_{1} + C_{2}$$

B
$$C_{1} - C_{2}$$

C
$$\dfrac {C_{1}C_{2}}{C_{1} + C_{2}}$$

D
$$\dfrac {C_{1} + C_{2}}{C_{1}C_{2}}$$

Solution
Question 7
1 / -0

When two capacitors are connected in parallel the resulting combination has capacitance $$10uF$$. The same capacitors when connected in series results in a capacitance $$0.5uF$$. The respective values of individual capacitors are

A
$$1.9uF$$ and $$0.2uF$$

B
$$(8+2\sqrt{5})uF$$ and $$(2-2\sqrt{5})uF$$

C
$$(5+2\sqrt{5})uF$$ and $$(5-2\sqrt{5})uF$$

D
$$12uF$$ and $$17uF$$

E
$$5uF$$ and $$2uF$$

Solution

When capacitors are connected in parallel then $$C_{eq}=C_1+C_2=10uF$$.......(i)
When capacitors are connected in series
then $$C_{eq}=\dfrac{C_1C_2}{C_1+C+2}=0.5uF$$
or $$C_1C_2=0.5(C_1+C_2)$$
or $$C_1C_2=5(uF)^2$$......(ii)
$$(\because C_1+C_2=10uF)$$
$$\because (C_1+C_2)^2=C^2_1+C^2_2-2C_1C_2$$.........(iii)
$$(C_1-C_2)^2=C^2_1+C^2_2+C^2_2-2C_1C_2$$..........(iv)
Put the value from Equations (i) and (ii) in the equation (iii)

Hence, $$C^2_1+C^2_2=(10u)^2-2\times 5u^2=90u^2$$
Put the above value in Equation (iv)
$$(C_1-C_2)^2=90u^2-2\times 5u^2=80u^2$$
$$\therefore C_1-C_2=\sqrt{5}u$$............(v)
Now from Equations (i) and (v),
$$C_1=\dfrac{10+4\sqrt{5}}{2}=(5+2\sqrt{5})uF$$
$$C_2=\dfrac{10-4\sqrt{5}}{2}=(5-2\sqrt{5})uF$$
Question 8
1 / -0

Energy stored per unit volume of a parallel plate capacitor having plate area A and plate separation d charged to a potential V volt is

A
$$ \dfrac {1}{2} C^2V^2 $$

B
$$ \dfrac {q^2}{4C} $$

C
$$ \dfrac {1}{2} \varepsilon _ o \left( \dfrac { V }{ d } \right) $$

D
$$ \dfrac {1}{2} \varepsilon _ o \left( \dfrac { V^2 }{ d^2 } \right) $$
Question 9
1 / -0

A neutral spherical copper particle has a radius of $$10\ nm (1nm = 10^{-9}m)$$. It gets charged by applying the voltage slowly adding one electron at a time. Then the graph of the total charge on the particle vs the applied voltage would look like:

A

B

C

D

Solution

For spherical surface
Potnetial $$V=\dfrac{kQ}{r}$$
$$\because$$ charge increases in discrete manner, so till the time charge is same on sphere, the potential will remain same.
Question 10
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Five identical capacitors, of capacitance $$20\mu F$$ each, are connected to a battery of $$150V$$, in a combination as shown
in the diagram. What is the total amount of charge stored?

A
$$15\times 10^{-3}C$$

B
$$12\times 10^{-3}C$$

C
$$10\times 10^{-3}C$$

D
$$3\times 10^{-3}C$$

Solution