Parallel and Series Combination of Capacitors

Q. Two capacitors of capacitance $1\mu \text{F}$ and $2\mu \text{F}$ are charged to potential difference $20\text{V}$ and $15\text{V}$ as shown in figure. If now terminal $\text{B}$ and $\text{C}$ are connected together while terminal $\text{A}$ is connected with positive terminal of battery and terminal $\text{D}$ of capacitor connected with negative terminal of battery with an emf $30\text{V}$.


The final charges on $1\mu \text{F}$ and $2\mu \text{F}$ capacitors respectively will be;

1. $\frac{50}{3}\mu \text{C},\frac{80}{3}\mu \text{C}$
2. $\frac{50}{6}\mu \text{C},\frac{40}{3}\mu \text{C}$
3. $\frac{20}{3}\mu \text{C},\frac{80}{3}\mu \text{C}$
4. $\frac{120}{7}\mu \text{C},\frac{80}{7}\mu \text{C}$

Q.

A parallel plate capacitor of area A, plate separation d and capacitance C is filled with three different dielectric materials having dielectric constants $K_1,K_{2}and{K}_3$ as shown in Fig. If a single dielectric material is to be used to have the same capacitance C in this capacitor, then its dielectric constant K is given by

1. $\frac{1}{K}=\frac{1}{K_1}+\frac{1}{K_2}+\frac{1}{2K_3}$
   

2. $\frac{1}{K}=\frac{1}{K_1+K_2}+\frac{1}{2K_3}$
   

3. $K=\frac{K_1{K}_2}{K_1+K_2}+2K_3$
   

4. $K=K_1+K_2+K_3$

Q. A point charge +2Q is placed just inside a cube corner on the body diagonal of the cube. If electric flux passing through any of the adjacent face (close to the charge) is 7Q/kEo , then value of k is _____.

Q.

Write a function rule for “the output is one-third of the input.”

Q. A copper wire of cross-sectional area 0.01 cm² is under a tension of 20N. Find the decrease in the cross-sectional area. Young modulus of copper = 1.1 × 10¹¹ N m⁻² and Poisson ratio = 0.32.

Q. All plates are of same area (A). Find effective capacitance between A & B

1. $\frac{3}{5}\frac{{ϵ}_{0}A}{d}$
2. $\frac{5}{3}\frac{{ϵ}_{0}A}{d}$
3. $\frac{4}{3}\frac{{ϵ}_{0}A}{d}$
4. $4\frac{{ϵ}_{0}A}{d}$

Q.

The circuit shown contains four condensers each of capacity "C”. The equivalent capacity between the terminals P and Q shown is

1. C

2. C/ 2

3. 2 C

4. zero

Q.

Write a function rule for “the output is one-fourth of the input.”

Q. Each resistor shown in the figure is an infinite network of resistance $1\Omega$. The effective resistance between points $\text{A}$ and $\text{B}$ is
($\sqrt{3}=1.73$)

1. Less than $1\Omega$
2. $1\Omega$
3. $3\Omega$
4. More than $1\Omega$ but less than $3\Omega$

Q.

Four metal plates numbered 1, 2, 3 and 4 are arranged as shown in Fig. The area of each plate is A and the separation between the plates is d. The capacitance of the arrangement is

1. $\frac{{\epsilon }_{0}A}{d}$
   

2. $\frac{2{\epsilon }_{0}A}{d}$
   
   

3. $\frac{3{\epsilon }_{0}A}{d}$
   

4. $\frac{4{\epsilon }_{0}A}{d}$

Q. Four condensers each of capacity 4μF are connected as shown in figure. V_P-V_Q=15volts . The energy stored in the system is [CPMT 1976, 89]

1. 2400ergs

2. 1800ergs

3. 3600ergs

4. 5400ergs

Q. The equivalent capacitance between A and B in the given circuit is

1. $4\mu F$
2. $22\mu F$
3. $16\mu F$
4. $6\mu F$

Q. What is the effective capacitance between points $X$ and $Y?$

1. $12\mu F$
2. $18\mu F$
3. $24\mu F$
4. $6\mu F$

Q. 3- The value of the permittivity of vacuurm in sys te m is 8-85 70-12- Its value in a new, systern of units iwhich Unit or lengthmetre Unit oF msaSS_ Unit of time2 sec Kg 2 Unit of current22 ampill be CT) 443 x 1O-1a (3) 1-77×10-11 C4 8-85*1O 12

Q. Given $C_1=C_5=C_3=2\mu F,C_2=C_4=4\mu F$.
$2\mu F$ can withstand maximum voltage of $5V$ and $4\mu F$ can withstand maximum of $10V$. Which of the capacitors will burn?

1. All
2. $C_1$ and $C_2$
3. $C_1$ and $C_5$
4. $C_1,C_2$ and $C_5$

Q.

Following figure shows a network of capacitors where the numbers indicate capacitance in $\mu F.$ The equivalent capacitance between points A and B is

1. $\frac{28}{9}\mu F$
   

2. $\frac{32}{9}\mu F$
   

3. $4\mu F$
   

4. $\frac{40}{9}\mu F$

Q. Find equivalent capacitance between $A$ and $B$

1. $5\mu F$
2. $4\mu F$
3. $3\mu F$
4. $2\mu F$

Q. A parallel plate capacitor of capacitance $C$ is connected to a battery and is charged to a potential difference $V$. Another capacitor of capacitance $2C$ is similarly charged to a potential difference $2V$. The charging battery is now disconnected, and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. Find heat dissipated in the system ?

1. Zero
2. $3C{V}^2$
3. $\frac{9}{2}C{V}^2$
4. $\frac{5}{2}C{V}^2$

Q. Two parallel plate capacitors ($AB\&CD$) differ only in the spacing between their plates(very thin).
Capacitor $AB$ has a spacing of $5\text{mm}$ and a capacitance of $20\text{pF}$, the capacitor $CD$, has a spacing of $2\text{mm}$.
Plates $A$ and $C$ carry charges of $+1\text{nC}$, while $B$ and $D$ each carry $-1\text{nC}$.
If the capacitor $CD$ is slid centrally between and parallel to the plates of $AB$ without touching them (as shown below), what is the potential difference $V_{AB}$ ?

1. $70\text{V}$
2. $50\text{V}$
3. $40\text{V}$
4. None of these

Q. Two parallel plate capacitors $\text{A}$ and $\text{B}$ having capacitances $4\mu \text{F}$ and $6\mu \text{F}$ are seperately charged upto $10\text{V}$ and $5\text{V}$ respectively. Now positive plate of $\text{A}$ is connected to the positive plate of $\text{B}$ and negative plate of $\text{A}$ is connected with negative plate of $\text{B}$. Find the final charge on each capacitor ?

1. $40\mu \text{C}$, $30\mu \text{C}$
2. $20\mu \text{C}$, $50\mu \text{C}$
3. $35\mu \text{C}$, $35\mu \text{C}$
4. $28\mu \text{C}$, $42\mu \text{C}$

Q. Find equivalent capacitance between $A$ and $B$. [Assume each conducting plate is having same dimensions and neglect the thickness of the plate, $\frac{{ϵ}_{0}A}{d}=7\mu F$ where $A$ is area of plates, $A>>d$]

1. $7\mu F$
2. $11\mu F$
3. $12\mu F$
4. $14\mu F$

Q.

1. 27

2. 59

3. 32

4. 72

Q. If in the infinite series circuit, C = 9 $\mu$F and $C_1=6\mu F$then the capacity across AB is

1. $1.25\mu F$
2. $6\mu F$
3. $3\mu F$
4. $12\mu F$

Q. $V_A-V_B$ of given circuit is [in volts]

Q.

Three condensers C1, C2 and C3 are connected as shown to a battery. Which of them get charged by the battery?

1. $C_1$only

2. $C_2$and $C_3$only

3. $C_1$and $C_3$only

4. $C_1$, $C_2$ and $C_3$

Q. Find the equivalent resistance between points $M$ and $N$ in the circuit shown in figure.

1. $\frac{r}{6}$
2. $\frac{2r}{3}$
3. $3r$
4. $\frac{r}{2}$

Q. In the given circuit the potential difference across the $4.5\mu F$ capacitor is

1. $\frac{8}{3}\text{V}$
2. $4\text{V}$
3. $6\text{V}$
4. $8\text{V}$

Q. Each resistor shown in the figure is an infinite network of resistance $1\Omega$. The effective resistance between points $\text{A}$ and $\text{B}$ is
($\sqrt{3}=1.73$)

1. Less than $1\Omega$
2. More than $1\Omega$ but less than $3\Omega$
3. $3\Omega$
4. $1\Omega$

Q. A battery of 10 V is connected to a condenser of capacity 100 mF. The battery is removed and the condenser is connected to an identical uncharged condenser. It is found that the charge distributes equally on these two condensers. The common potential of the system is?

1. 10V
2. 5V
3. 20V
4. 2.5V

Q.

What is the equivalent capacitance between points A and B?

1. 10 nF

2. 12 nF

3. 0.78 nF

4. 0. 68 nF