Question 1

Consider two uncharged capacitors of equal capacitance 200 pF. One of them is charged by a 100 V supply and disconnected. Now this capacitor is connected to the uncharged capacitor. The amount of elec

Accepted Answer

Initial energy of the charged capacitor is given by U_i = 1 2 CV^2. When it is connected to an identical uncharged capacitor, the common potential becomes V' = CV C+C = V 2 . Final energy of the system is U_f = 1 2 (2C)V'^2 = 1 2 (2C) ( V 2 )^2 = 1 4 CV^2. Energy lost during the process is U = U_i - U_f = 1 2 CV^2 - 1 4 CV^2 = 1 4 CV^2. Substituting the given values C = 200 10^ -12 F and V = 100 V: U = 1 4 200 10^ -12 (100)^2 U = 50 10^ -12 10^4 = 0.5 10^ -6 J. Answer: 0.5 10^ -6 J

Question 2

Five capacitors of capacitances C_1 = C_2 = C_3 = C_4 = 10\ F and C_5 = 2.5\ F are connected as shown, along with a battery of 50 V. The equivalent capacitance and the charges on each capacitor respec

Accepted Answer

From the given circuit diagram, the capacitors C_1, C_2, C_3, and C_4 are connected in series. This series combination is connected in parallel with the capacitor C_5. The entire combination is connected across the 50 V battery. Let C_s be the equivalent capacitance of the series branch containing C_1, C_2, C_3, and C_4. 1 C_s = 1 C_1 + 1 C_2 + 1 C_3 + 1 C_4 1 C_s = 1 10 + 1 10 + 1 10 + 1 10 = 4 10 \ F ^ -1 C_s = 2.5\ F The total equivalent capacitance C_ eq of the circuit is the sum of the para

Question 3

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 th

Accepted Answer

From the given circuit diagram, capacitors P and Q are connected in series, and their combination is connected in parallel with capacitor S. The equivalent capacitance of the series combination of P and Q is: C_ PQ = C C C + C = C 2 The total equivalent capacitance of the system is: C_ eq = C_ PQ + C_S = C 2 + C = 3C 2 The total energy stored in the system is: U_T = 1 2 C_ eq V^2 = 1 2 ( 3C 2 ) V^2 = 3 4 C V^2 Since capacitors P and Q are identical and connected in series across the battery of v

Question 4

The plates of a parallel plate capacitor are separated by d. Two slabs of different dielectric constant K_1 and K_2 with thickness 3 8 d and d 2 , respectively are inserted in the capacitor. Due to th

Accepted Answer

C_1= _0 A / d aligned & C _2= _0 ~A 3 ~d 8 ~K _1 + d 2 ~K _2 + ( d - 3 ~d 8 - d 2 ) \ & C _2= _0 ~A / d 3 8 ~K _1 + 1 2 ~K _2 + 1 8 \ & = _0 ~A / d 3 8 ~K _1 + 1 2 ( 4 5 ~K _1 ) + 1 8 \ & C _2=2 C _1 \ & _0 ~A / d 3 8 ~K _1 + 5 8 ~K _1 + 1 8 =2 _0 ~A / d \ & 1 1 ~K _1 + 1 8 =2 1 ~K _1 + 1 8 = 1 2 ~K _1= 8 3 =2.66 aligned

Question 5

The steady state current in| the circuit shown below is :

Accepted Answer

At steady state, capacitor will be completely charged and will not allow current to pass through it. The simplified circuit will be : i= V R i= 10 2+3 =2 ~A

Question 6

A 12 pF capacitor is connected to a 50 V battery, the electrostatic energy stored in the capacitor in nJ is

Accepted Answer

Electrostatic energy stored U= 1 2 C V^2 = 1 2 12 10^ -12 (50)^2 =6 25 10^ -10 =15 10^ -9 ~J =15 ~nJ

Question 7

The capacitance of a capacitor with charge q and a potential difference V depends on

Accepted Answer

Capacitance of capacitor C= A _0 d so capacitance of capacitor is independent of charge (q) and potential (V), it depends on geometry of the capacitor and medium between plates of the capacitor.

Question 8

If the plates of a parallel plate capacitor connected to a battery are moved close to each other, then A. the charge stored in it, increases. B. the energy stored in it, decreases. C. its capacitance

Accepted Answer

Given V=V= Constant (i) aligned & C^ = _0 A d^ , C= _0 A d \ & d^ d \ & C^ aligned Hence, final capacitance greater than initial capacitance, (ii) aligned U^ & = 1 2 C^ V^2 \ U & = 1 2 C V^2 \ U^ & aligned Hence final energy is greater than initial energy (iii) aligned & Q^ V^ =C^ and Q V =C \ & Q^ V^ Q V aligned (iv) Product of charge and voltage aligned & X^ =Q^ V=C^ V^2 \ & X=Q V=C V^2 \ & X^ aligned

Question 9

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

Accepted Answer

Given circuit is balanced Wheatstone bridge aligned C_ A B & =1+1 \ & =2 F aligned

Question 10

Given below are two statements: Statement I : The Indian Government has set up GEAC, which will make decisions regarding the validity of GM research. Statement II : Biopiracy is the term used to refer

Accepted Answer

Option (1) is the correct answer because Indian Government has set up organisations such as GEAC (Genetic Engineering Approval Committee), which will make decisions regarding the validity of GM research and the safety of introducing GM-organisms for public services and Biopiracy is used to refer to the use of bioresources by multinational companies and other organisations without proper authorisation from the countries and people concerned without compensatory payment, thus statement I is true b

Capacitance — Previous Year Questions & Solutions