Question

Case study:Read the following paragraph and answers the questions:

An arrangement of two conductors separated by an insulating medium can be used to store electric charge and electric energy. Such a system is called a capacitor. The more charge a capacitor can store, the greater is its capacitance. Usually, a capacitor consists of two capacitors having equal and opposite charge + Q and –Q. Hence, there is a potential difference V between them. By the capacitance of a capacitor, we mean the ratio of the charge Q to the potential difference V. By the charge on a capacitor we mean only the charge Q on the positive plate. Total charge of the capacitor is Zero. The capacitance of a capacitor is a constant and depends on geometric factors, such as the shapes, sizes and relative positions of the two conductors, and the nature of the medium between them. The unit of capacitance is Farad (F). But μF and pF are the more convenient units commonly used. Capacitor consists of two long strips or metal foils, separated by two long strips of dielectrics, rolled up into a small cylinder. Common dielectric materials are plastics (such as polyestor and polycarbonates) and aluminium oxide. Capacitors are widely used in television, computer, and other electric circuits.

1. A parallel plate capacitor C has charge Q. The actual charge on its plates are: a. Q, Q
b. Q/2, Q/2
c. Q, –Q
d. Q/2, –Q/2

2. A parallel plate capacitor is charged. If the plate are pulled apart,
a. the capacitance increases.
b.the potential difference increases.
c. the total charge increases.
d. the charge and the potential difference remains the same.

3. If n capacitors, each of capacitance C, are connected in series, then the equivalent capacitance of the combination will be.
a. n C
b. n^2 C
c. C/n
d. C/n^2

4. Three capacitors 2.0, 3.0 and 6.0 microfarad are connected in series to a 10Vsource. The charge( in μC) on the 3.0 microfarad capacitor is:

a. 5
b. 10
c. 15
d. none of these

Answer 1

Explanation:

Case study:Read the following paragraph and answers the questions:

An arrangement of two conductors separated by an insulating medium can be used to store electric charge and electric energy. Such a system is called a capacitor. The more charge a capacitor can store, the greater is its capacitance. Usually, a capacitor consists of two capacitors having equal and opposite charge + Q and –Q. Hence, there is a potential difference V between them. By the capacitance of a capacitor, we mean the ratio of the charge Q to the potential difference V. By the charge on a capacitor we mean only the charge Q on the positive plate. Total charge of the capacitor is Zero. The capacitance of a capacitor is a constant and depends on geometric factors, such as the shapes, sizes and relative positions of the two conductors, and the nature of the medium between them. The unit of capacitance is Farad (F). But μF and pF are the more convenient units commonly used. Capacitor consists of two long strips or metal foils, separated by two long strips of dielectrics, rolled up into a small cylinder. Common dielectric materials are plastics (such as polyestor and polycarbonates) and aluminium oxide. Capacitors are widely used in television, computer, and other electric circuits.

1. A parallel plate capacitor C has charge Q. The actual charge on its plates are: a. Q, Q

b. Q/2, Q/2

c. Q, –Q

d. Q/2, –Q/2

2. A parallel plate capacitor is charged. If the plate are pulled apart,

a. the capacitance increases.

b.the potential difference increases.

c. the total charge increases.

d. the charge and the potential difference remains the same.

3. If n capacitors, each of capacitance C, are connected in series, then the equivalent capacitance of the combination will be.

a. n C

b. n^2 C

c. C/n

d. C/n^2

4. Three capacitors 2.0, 3.0 and 6.0 microfarad are connected in series to a 10Vsource. The charge( in μC) on the 3.0 microfarad capacitor is:

a. 5

b. 10

c. 15

d. none of these

Answer 2

The correct option to the following questions are given below-

1. The correct option is (c), which is Q, -Q - When a capacitor is connected to the battery of potential difference V. It produces a charge Q to the capacitor. Then, on each capacitor, the charge will be equal and opposite and its magnitude will be the same as the charge it stores.
2. The correct option is (b), which is the potential difference increases. The capacitance of the parallel plate capacitor is - C=ε0AdC=ε0Ad . A parallel plate capacitor is charged (battery is disconnected) then the plates are pulled apart, the capacitance decreases while the charge remains the same  As Potential difference=Charge×Capacitance  Therefore, potential difference increases
3. The correct option is (c), which is C/n. When n capacitor of capacitance is connected in series, the equivalent capacitance will be C/n.
4. The correct option is (D)

       Given: capacitance = 2μF, 3μF, 4μF

                   Potential difference = 10V

       To find: Charge on 3 μF

        Solution: Total capacitance will be, 1/C = 1/2 + 1/3 + 1/4

                         C = 12/13 μF

                        total charge Q = CV

                                              Q = 12/13 × 10

                                               Q = 120/13 μC

                     The charge will be the same when connected in series therefore, the charge in 3 μF will be 120/13 μC.