Combination of Capacitors

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JEE Advanced 2013

In the circuit shown in the figure, there are two parallel plate capacitors each of capacitance $C$ . The switch $S_{1}$ is pressed first to fully charge the capacitor $C_{1}$ and then released. The switch $S_{2}$ is then pressed to charge the capacitor $C_{2}$ . After some time, $S_{2}$ is released and then $S_{3}$ is pressed. After some time (2013 Adv.)

C_{1}

2 C V_{0}

(B)

the charge on the upper plate of

C_{1}

C V_{0}

(C)

the charge on the upper plate of

C_{2}

is 0

(D)

the charge on the upper plate of

C_{2}

- C V_{0}

LEVELJEE Main

Five identical capacitor plates, each of area $A$ , are arranged such that adjacent plates are at a distance $d$ apart, the plates are connected to a source of emf $V$ as shown in the figure. The charge on plate 1 is ...... and on plate 4 is .......

JEE Main 2012

LEVELJEE Main

In the given circuit, a charge of $+ 80 μ C$ is given to the upper plate of the $4 μ F$ capacitor. Then in the steady state, the charge on the upper plate of the $3 μ F$ capacitor is

(A)

+ 32 μ C

(B)

+ 40 μ C

(C)

+ 48 μ C

(D)

+ 80 μ C

LEVELJEE Main

Seven capacitors each of capacitance $2 μ F$ are connected in a configuration to obtain an effective capacitance $\frac{10}{11} μ F$ . Which of the following combination will achieve the desired result ?

Consider the situation shown in the figure. The capacitor $A$ has a charge $q$ on it whereas $B$ is uncharged. The charge appearing on the capacitor $B$ a long time after the switch is closed is

(A)

zero

(B)

q /2

(C)

q

(D)

2 q

JEE Advanced 1988

LEVELJEE Main

Two parallel plate capacitors of capacitances $C$ and $2 C$ are connected in parallel and charged to a potential difference $V$ . The battery is then disconnected and the region between the plates of capacitor $C$ is completely filled with a material of dielectric constant $K$ . The potential difference across the capacitors now becomes....

JEE Advanced 1993

LEVELJEE Advanced

Two parallel plate capacitors $A$ and $B$ have the same separation $d = 8.85 \times 1 0^{- 4} m$ between the plates. The plate areas of $A$ and $B$ are $0.04 m^{2}$ and $0.02 m^{2}$ respectively. A slab of dielectric constant (relative permittivity) $K = 9$ has dimensions such that it can exactly fill the space between the plates of capacitor $B$ . (a) The dielectric slab is placed inside $A$ as shown in figure (i). $A$ is then charged to a potential difference of $110 V$ . Calculate the capacitance of $A$ and the energy stored in it. (b) The battery is disconnected and then the dielectric slab is removed from $A$ . Find the work done by the external agency in removing the slab from $A$ . (c) The same dielectric slab is now placed inside $B$ , filling it completely. The two capacitors $A$ and $B$ are then connected as shown in figure (iii). Calculate the energy stored in the system.

LEVELJEE Main

Find the potential difference between the points A and B and between the points B and C in the steady state.

LEVELJEE Advanced

Two capacitors $A$ and $B$ with capacities $3 μ F$ and $2 μ F$ are charged to a potential difference of $100 V$ and $180 V$ respectively. The plates of the capacitors are connected as shown in the figure with one wire of each capacitor free. The upper plate of $A$ is positive and that of $B$ is negative. An uncharged $2 μ F$ capacitor $C$ with lead wires falls on the free ends to complete the circuit. Calculate (a) the final charge on the three capacitors and (b) the amount of electrostatic energy stored in the system before and after completion of the circuit.

JEE Advanced 2024

LEVELJEE Advanced

Four identical thin, square metal sheets, $S_{1}$ , $S_{2}$ , $S_{3}$ and $S_{4}$ , each of side $a$ are kept parallel to each other with equal distance $d$ ( $<< a$ ) between them, as shown in the figure. Let $C_{0} = ε_{0} a^{2} / d$ , where $ε_{0}$ is the permittivity of free space. Match the quantities mentioned in List-I with their values in List-II and choose the correct option.

List-I

(P)

The capacitance between

S_{1}

and

S_{4}

, with

S_{2}

and

S_{3}

not connected, is

(Q)

The capacitance between

S_{1}

and

S_{4}

, with

S_{2}

shorted to

S_{3}

, is

(R)

The capacitance between

S_{1}

and

S_{3}

, with

S_{2}

shorted to

S_{4}

, is

(S)

The capacitance between

S_{1}

and

S_{2}

, with

S_{3}

shorted to

S_{1}

, and

S_{2}

shorted to

S_{4}

, is

List-II

(1)

3 C_{0}

(2)

C_{0} /2

(3)

C_{0} /3

(4)

2 C_{0} /3

(5)

2 C_{0}

JEE Main 2017

LEVELJEE Advanced

A capacitance of $2 μ F$ is required in an electrical circuit across a potential difference of $1 kV$ . A large number of $1 μ F$ capacitors are available which can withstand a potential difference of not more than $300 V$ . The minimum number of capacitors required to achieve this is

Figure shows charge ( $q$ ) versus voltage ( $V$ ) graph for series and parallel combination of two given capacitors. The capacitances are

(A)

60 μ F

and

40 μ F

(B)

50 μ F

and

30 μ F

(C)

20 μ F

and

30 μ F

(D)

40 μ F

and

10 μ F

LEVELJEE Main

A parallel plate capacitor with air between the plates has a capacitance of $9 pF$ . The separation between its plates is $d$ . The space between the plate is now filled with two dielectrics. One of the dielectrics has dielectric constant $K_{1} = 3$ and thickness $d /3$ while the other one has dielectric constant $K_{2} = 6$ and thickness $2 d /3$ . Capacitance of the capacitor is now

(A)

1.8 pF

(B)

45 pF

(C)

40.5 pF

(D)

20.25 pF

JEE Main 2021

LEVELJEE Main

Two capacitors of capacities $2 C$ and $C$ are joined in parallel and charged upto potential $V$ . The battery is removed and the capacitor of capacity $C$ is filled completely with a medium of dielectric constant $K$ . The potential difference across the capacitors will now be

(A)

\frac{V}{K + 2}

(B)

\frac{V}{K}

(C)

\frac{3 V}{K + 2}

(D)

\frac{3 V}{K}

JEE Main 2021

LEVELBoard

Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be

In the given circuit, charge $Q_{2}$ on the $2 μ F$ capacitor changes as $C$ is varied from $1 μ F$ to $3 μ F$ . $Q_{2}$ as a function of $C$ is given properly by (figures are drawn schematically and are not to scale)

Two capacitors $C_{1}$ and $C_{2}$ are charged to $120 V$ and $200 V$ , respectively. It is found that by connecting them together, the potential on each one can be made zero. Then,

(A)

5 C_{1} = 3 C_{2}

(B)

3 C_{1} = 5 C_{2}

(C)

3 C_{1} + 5 C_{2} = 0

(D)

9 C_{1} = 4 C_{2}

JEE Main 2020

LEVELJEE Main

Effective capacitance of parallel combination of two capacitors $C_{1}$ and $C_{2}$ is $10 μ F$ . When these capacitors are individually connected to a voltage source of $1 V$ , the energy stored in the capacitor $C_{2}$ is 4 times that of $C_{1}$ . If these capacitors are connected in series, then their effective capacitance will be

(A)

4.2 μ F

(B)

3.2 μ F

(C)

1.6 μ F

(D)

8.4 μ F

LEVELJEE Main

A parallel plate capacitor is made by stacking $n$ equally spaced plates connected alternatively. If the capacitance between any two adjacent plates is $C$ , then the resultant capacitance is

(A)

(n - 1) C

(B)

(n + 1) C

(C)

C

(D)

n C

JEE Main 2019

LEVELJEE Main

In the figure shown, after the switch 'S' is turned from position 'A' to position 'B', the energy dissipated in the circuit in terms of capacitance 'C' and total charge 'Q' is

(A)

\frac{3}{4} \cdot \frac{Q ^{2}}{C}

(B)

\frac{5}{8} \cdot \frac{Q ^{2}}{C}

(C)

\frac{1}{8} \cdot \frac{Q ^{2}}{C}

(D)

\frac{3}{8} \cdot \frac{Q ^{2}}{C}

JEE Main 2019

LEVELJEE Main

The parallel combination of two air filled parallel plate capacitors of capacitance $C$ and $n C$ is connected to a battery of voltage, $V$ . When the capacitors are fully charged, the battery is removed and after that a dielectric material of dielectric constant $K$ is placed between the two plates of the first capacitor. The new potential difference of the combined system is

(A)

\frac{( n + 1 ) V}{( K + n )}

(B)

\frac{nV}{K + n}

(C)

V

(D)

\frac{V}{K + n}

JEE Main 2020

LEVELJEE Main

Two capacitors of capacitances $C$ and $2 C$ are charged to potential differences $V$ and $2 V$ respectively. These are then connected in parallel in such a manner that the positive terminal of one is connected to the negative terminal of the other. The final energy of this configuration is

(A)

\frac{9}{2} C V^{2}

(B)

\frac{3}{2} C V^{2}

(C)

\frac{25}{6} C V^{2}

A $60 pF$ capacitor is fully charged by a $20 V$ supply. It is then disconnected from the supply and is connected to another uncharged $60 pF$ capacitor in parallel. The electrostatic energy that is lost in this process by the time, the charge is redistributed between them is (in $nJ$ )

JEE Main 2020

LEVELJEE Main

A capacitor $C$ is fully charged with voltage $V_{0}$ . After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance $\frac{C}{2}$ . The energy loss in the process after the charge is distributed between the two capacitors is

(A)

\frac{1}{3} C V_{0}^{2}

(B)

\frac{1}{6} C V_{0}^{2}

(C)

\frac{1}{2} C V_{0}^{2}

(D)

\frac{1}{4} C V_{0}^{2}

LEVELBoard

If there are $n$ capacitors in parallel connected to $V$ volt source, then the energy stored is equal to

(A)

C V

(B)

\frac{1}{2} n C V^{2}

(C)

C V^{2}

(D)

\frac{1}{2 n} C V^{2}

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } In the given circuit, a charge of +80μC is given to the upper plate of the 4μF capacitor. Then in the steady state, the charge on the upper plate of the 3μF capacitor is

Find the potential difference between the points A and B and between the points B and C in the steady state.

List-I

List-II

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Figure shows charge (q) versus voltage (V) graph for series and parallel combination of two given capacitors. The capacitances are

Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Two capacitors C1​ and C2​ are charged to 120 V and 200 V, respectively. It is found that by connecting them together, the potential on each one can be made zero. Then,

In the figure shown, after the switch 'S' is turned from position 'A' to position 'B', the energy dissipated in the circuit in terms of capacitance 'C' and total charge 'Q' is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If there are n capacitors in parallel connected to V volt source, then the energy stored is equal to

In the given circuit, a charge of $+ 80 μ C$ is given to the upper plate of the $4 μ F$ capacitor. Then in the steady state, the charge on the upper plate of the $3 μ F$ capacitor is

Figure shows charge ( $q$ ) versus voltage ( $V$ ) graph for series and parallel combination of two given capacitors. The capacitances are

Two capacitors $C_{1}$ and $C_{2}$ are charged to $120 V$ and $200 V$ , respectively. It is found that by connecting them together, the potential on each one can be made zero. Then,

If there are $n$ capacitors in parallel connected to $V$ volt source, then the energy stored is equal to