Combination of Capacitors

Capacitors of capacities $C_1$ and $C_2$ are connected in series. If the combination is connected to a supply of V volt then the potential difference across capacitor $C_2$ is

Four parallel plate capacitors are connected in parallel. Each capacitor has a plate area $\frac{A}{4}$ and the separation between the plates is $d, 2d, 3d$ and $4d$ respectively. The equivalent capacity of the combination is [$\varepsilon_0 =$ permittivity of free space]

Two parallel plate air capacitors are connected in parallel. Each capacitor has plate area $A/2$ and separation between the plates is $d$ and $2d$ respectively. The equivalent capacity of the combination is

( $\epsilon_0$ = absolute permittivity of free space)

Three parallel plate air capacitors are connected in parallel. Each capacitor has plate area A/3 and separation between the plates is d, 2d and 3d respectively. The equivalent capacity of the combination is ($\epsilon_0$-permittivity of free space)

Three identical capacitors connected in series have net capacitance '$x$'. Then they are connected in parallel. The ratio of energy stored in series configuration to that in parallel configuration is (if both configurations are connected to the same source)

Three capacitors $C_1, C_2$ and $C_3$ are connected to voltage source V as shown in figure. The voltage across $C_3$ will be

Initially, 'n' identical capacitors are joined in parallel, are charged to potential 'V'. Now they are separated and joined in series. Then

Figure shows a network of five capacitors connected to a supply voltage 'V'. The equivalent capacitance and the energy stored in the network is respectively

Two capacitors, $C_1$ and $C_2$ have their capacitances in the ratio 1:2. $V_s$ and $V_p$ are the potential differences applied across the series and parallel combination of $C_1$ and $C_2$ respectively, so that the energy stored in the two cases becomes same. The ratio $V_s$ to $V_p$ is

The potential difference that must be applied across the parallel and series combination of three identical capacitors such that the energy stored in them becomes the same. The ratio of potential difference in parallel to series combination is

Three identical capacitors, $P, Q$ and $S$, each of the capacitance $C$, are connected to a battery of voltage $V$, as shown in the figure. If the energy stored in the capacitor $P$ and total energy stored in the system are $U_P$ and $U_T$, respectively, then the ratio $\frac{U_P}{U_T}$ is:

Four capacitors each of $16\ \mu\text{F}$ are connected as shown. The capacitance between points $A$ and $B$ is (in $\mu\text{F}$)

What will be the charge on any one of the $4\ \mu\text{F}$ capacitors and $2\ \mu\text{F}$ capacitor in $\mu\text{C}$?

If the equivalent capacitance between points A and B of the combination of capacitors shown in figure, is 6C, the capacitor $C'$ is

Four capacitors are connected to a battery as shown in figure. The ratio of charges on capacitors $C_2$ and $C_4$ is

Five capacitors of capacitances

$C_1 = C_2 = C_3 = C_4 = 10\ \mu\text{F}$ and $C_5 = 2.5\ \mu\text{F}$ are connected as shown, along with a battery of 50 V.

The equivalent capacitance and the charges on each capacitor respectively are:

From the circuit given below, the capacitance between terminals $A$ and $B$ shown in the circuit is $\underline{\qquad}\ \mu\text{F}$.

(take $C_1 = C_2 = C_3 = 1\ \mu\text{F}$ and $C_4 = 2\ \mu\text{F}$.)

Three capacitors each of capacitance ' C ' and breakdown voltage ' $V$ ' are connected in series. The capacitance and breakdown voltage of the series combination will be respectively

Seven capacitors each of capacitance $2\ \mu\text{F}$ are to be connected in a configuration to obtain an effective capacitance $\left(\frac{10}{11}\right)\mu\text{F}$. The combination is

Initially $n$ identical capacitors are joined in parallel and are charged to potential V. Now they are separated and joined in series. Then

A series combination of 10 capacitors, each of value ' $C_1$ ' is charged by a source of potential difference ' 4 V '. When another parallel combination of 8 capacitors, each of value ' $C_2$ ' is charged by a source of potential difference ' V ', it has the same total energy stored in it as in the first combination. The value of ' $C_2$ ' is

Two capacitors $C_1$ and $C_2$ are connected in parallel to a battery. Charge-time graph is shown below for the two capacitors. The energy stored with them are $U_1$ and $U_2$, respectively. Which of the given statements is true?

The potential difference across the 4 μF capacitor in the following circuit is

Three capacitors are connected to a battery as shown in figure. The ratio of charge on capacitors $C_3$ and $C_1$ is

Five capacitors, each of capacity ' $C$ ' are connected as shown in the figure. The resultant capacity between A and B is $14\ \mu\text{F}$. The capacity of each capacitor is

The equivalent capacitance between plates ' A ' and ' B ' ( A -area of each plate, d-separation between plates) ( $\varepsilon_0$ - permittivity of free space) is

Four capacitors each of capacitance $16\ \mu\text{F}$ are connected as shown in the figure. The capacitance between points $A$ and $B$ is: _________ (in $\mu\text{F}$).

Five capacitors, each of capacitance ' $C$ ' are connected as shown in the figure. The ratio of equivalent capacitance between P and R and the equivalent capacitance between P and Q is

Three condensers of capacities ' $C_1$ ', ' $C_2$ ', ' $C_3$ ' are connected in series with a source of e.m.f. ' $V$ '. The potentials across the three condensers are in the ratio

When three capacitors of equal capacities are connected in parallel and one of the same capacity, capacitor is connected in series with the combination. The resultant capacity is $4.5\ \mu\text{F}$. The capacity of each capacitor is

Seven capacitors each of capacitance $2\ \mu\text{F}$ are connected in a configuration to obtain an effective capacitance $\frac{6}{13}\ \mu\text{F}$. The combination which will achieve this will have

A series combination of $n_1$ capacitors, each of value $C_1$ is charged by a source of potential difference 6 V. Another parallel combination of $n_2$ capacitors, each of value $C_2$ is charged by a source of potential difference 2 V. Total energy of both the combinations is same. The value of $C_2$ in terms of $C_1$ is

The potential difference that must be applied across the series and parallel combination of 4 identical capacitors is such that the energy stored in them becomes the same. The ratio of potential difference in series to parallel combination is

Three capacitors of capacitances $25\ \mu\text{F}, 30\ \mu\text{F}$ and $45\ \mu\text{F}$ are connected in parallel to a supply of $100\text{ V}$. Energy stored in the above combination is E. When these capacitors are connected in series to the same supply, the stored energy is $\frac{9}{x}E$. The value of $x$ is _________.

In the circuit shown in the following figure, the potential difference cross $3\ \mu\text{F}$ capacitor is

In the following circuit, the equivalent capacitance between terminal A and terminal B is:

A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in figure. If the area of each stair is $\frac{A}{3}$ and the height is $d$, the capacitance of the arrangement is:

In the given figure, the charge stored in $6\ \mu\text{F}$ capacitor, when points $A$ and $B$ are joined by a connecting wire is __________ $\mu\text{C}$.

Two capacitors $C_1 = 3\ \mu\text{F}$ and $C_2 = 2\ \mu\text{F}$ are connected in series across d.c. source of $100\text{ V}$. The ratio of the potential across $C_2$ to $C_1$ is

Three identical capacitors of capacitance '$C$' each are connected in series and this connection is connected in parallel with one more such identical capacitor. Then the capacitance of whole combination is

Which of the following combination of 7 identical capacitors each of $2\ \mu\text{F}$ gives a capacitance of $\frac{10}{11}\ \mu\text{F}$?

Two condensers one of capacity $\frac{C}{2}$ and other capacity $C$ are connected to a battery of voltage $V$ as shown. The work done in charging fully both the condensers is

A parallel combination of two capacitors of capacities '$2C$' and '$C$' is connected across $5\text{ V}$ battery. When they are fully charged, the charges and energies stored in them be '$Q_1$ ', '$Q_2$' and '$E_1$ ', '$E_2$' respectively. Then $\frac{E_1-E_2}{Q_1-Q_2}$ in $\text{J/C}$ is (capacity is in Farad, charge in Coulomb and energy in J)

The ratio of potential difference that must be applied across parallel and series combination of two capacitors $C_1$ and $C_2$ with their capacitance in the ratio $1 : 2$ so that energy stored in these two cases becomes same is

In the given figure, the equivalent capacitance between points A and B is

In the given capacitive network the resultant capacitance between point $A$ and $B$ is

The equivalent capacity between terminal $A$ and $B$ is

The equivalent capacitance of the arrangement shown in figure is:

The equivalent capacitance of the system shown in the following circuit is:

The equivalent capacitance of the combination shown is:

In the given figure the total charge stored in the combination of capacitors is $100\ \mu\text{C}$. The value of ' $x$ ' is _________.

As shown in the figure, two parallel plate capacitors having equal plate area of $200\text{ cm}^{2}$ are joined in such a way that $a \neq b$. The equivalent capacitance of the combination is $x\epsilon_0\text{ F}$. The value of $x$ is ____________.

The effective capacitances of two capacitors are 3 $\mu$F and 16 $\mu$F, when they are connected in series and parallel respectively. The capacitance of two capacitors are:

The total charge on the system of capacitors $C_1 = 1\ \mu\text{F}, C_2 = 2\ \mu\text{F}, C_3 = 4\ \mu\text{F}$ and $C_4 = 3\ \mu\text{F}$ connected in parallel is:

(Assume a battery of $20\text{ V}$ is connected to the combination)

A source of potential difference $V$ is connected to the combination of two identical capacitors as shown in the figure. When key '$K$' is closed, the total energy stored across the combination is $E_1$. Now key '$K$' is opened and dielectric of dielectric constant 5 is introduced between the plates of the capacitors. The total energy stored across the combination is now $E_2$. The ratio $E_1/E_2$ will be:

The charge on capacitor of capacitance 15$\mu$F in the figure given below is:

Combination of four parallel plate air capacitors is shown in figure. Separation between the plate $P_1$ & $P_2$ is $\frac{d}{3}$ and separation between the plates $P_2$ and $P_3$ is $d$. The equivalent capacitance of the configuration is _______ $\mu\text{F}$.

(Given $\frac{\epsilon_0 A}{d} = 4\ \mu\text{F}$. Where A=Area of plates)

The equivalent capacitance between points A and B in below shown figure will be __________ $\mu$F.

A parallel plate capacitor is made up of stair like structure with a plate area A of each stair and that is connected with a wire of length b, as shown in the figure. The capacitance of the arrangement is $\frac{x}{15}\frac{\epsilon_0 A}{b}$. The value of x is ____________.

Capacitors of capacities $C_1, C_2$ and $C_3$ are connected in series. If the combination is connected to a supply of '$V$' volt, then potential difference across capacitor '$C_1$' is

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

Three capacitors C1 = 2$\mu$F, C2 = 6$\mu$F and C3 = 12$\mu$F are connected as shown in figure. Find the ratio of the charges on capacitors C1, C2 and C3 respectively:

Consider the combination of 2 capacitors C1 and C2 with C2 > C1, when connected in parallel, the equivalent capacitance is $\frac{15}{4}$ times the equivalent capacitance of the same connected in series. Calculate the ratio of capacitors, $\frac{C_2}{C_1}$.

The charge on each capacitor when a voltage source os 15 V is connected in the circuit as shown, is

In the given figure potential at point 'A' is 900 volt and point 'B' is earthed. What will be the potential at point 'P'?

The resultant capacity between points A and B in the given circuit is

In the arrangement of the capacitors as shown in figure, each capacitor is of 6 $\mu$F, then equivalent capacity between points A and B is

The equivalent capacitance of the combination shown in the figure is:

Four identical rectangular plates with length, l = 2 cm and breadth, b = $\frac{3}{2}$ cm are arranged as shown in figure. The equivalent capacitance between A and C is $\frac{x\varepsilon_0}{d}$. The value of x is ______________. (Round off to the Nearest Integer)

Two capacitors of capacities $2\ \mu\text{F}$ and $4\ \mu\text{F}$ are connected in parallel. A third capacitor of $6\ \mu\text{F}$ capacity is connected in series with this combination. A battery of 12 V is connected across this combination. The charge on $2\ \mu\text{F}$ capacitor is

Effective capacitance of parallel combination of two capacitors C1 and C2 is 10 μF. When these capacitors are individually connected to a voltage source of 1V, the energy stored in the capacitor C2 is 4 times that of C1. If these capacitors are connected in series, their effective capacitance will be:

Five capacitors each of capacity $C$ are connected as shown in figure. If their resultant capacity is $2\ \mu\text{F}$, then the capacity of each condenser is

In the circuit shown, charge on the 5 $\mu$F capacitor is:

In the circuit shown in the figure, the total charge is 750 $\mu$C and the voltage across capacitor C2 is 20 V. Then the charge on capacitor C2 is:

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

Which of the following combinations of 7 identical capacitors each of $2\ \mu\text{F}$ gives a resultant capacitance of $10/11\ \mu\text{F}$?

Seven capacitors, each of capacitance 2 $\mu$F, are to be connected in a configuration to obtain an effective capacitance of $\left(\frac{6}{13}\right)\mu\text{F}.$ Which of the combinations, shown in figures below, will achieve the desired value

In the given circuit, the charge on 4 $\mu$F capacitor will be:

In the circuit shown, find C if the effective capacitance of the whole circuit is to be 0.5 $\mu$F. All values in the circuit are in $\mu$F.

In the figure shown below, the charge on the left plate of the 10$\mu$F capacitor is –30$\mu$C. The charge on the right plate of the 6 $\mu$F capacitor is:

The equivalent capacitance between $A$ and $B$ in the circuit given below, is:

A capacitance of 2 $\mu$F is required in an electrical circuit across a potential difference of 1.0 kV. A large number of 1 $\mu$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:

Three capacitors each of 4 $\mu$F are to be connected in such a way that the effective capacitance is 6 $\mu$F. This can be done by connecting them:

Figure shows a network of capacitors where the numbers indicates capacitances in micro Farad. The value of capacitance C if the equivalent capacitance between point A and B is to be 1 $\mu$F is:

A combination of capacitors is set up as shown in the figure. The magnitude of the electric field, due to a point charge $Q$ (having a charge equal to the sum of the charges on the $4\ \mu\text{F}$ and $9\ \mu\text{F}$ capacitors), at a point distance $30\text{ m}$ from it, would equal:

In figure is shown a system of four capacitors connected across a 10 V battery. Charge that flow from switch S when it is closed is:

Three capacitances, each of 3 $\mu$F, are provided. These cannot be combined to provide the resultant capacitance of:

A series combination of n1 capacitors, each of value C1, is charged by a source of potential difference 4V. When another parallel combination of n2 capacitors, each of value C2, is charged by a source of potential difference V, it has the same (total) energy stored in it. as the first combination has. The value of C2. in terms of C1, is then

Three capacitors each of capacitance C and of breakdown voltage V are joined in series. The capacitance and breakdown voltages of the combination will be

Two condensers, one of capacity C and other of capacity C/2 are connected to a V-volt battery, as shown in the figure. The work done in charging fully both the condensers is

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