27 Lecture

A capacitor of capacitance 2 microfarads is charged to 100 V. The energy stored in the capacitor is:

a) 1 J

b) 2 J

c) 4 J

d) 10 J

Answer: c) 4 J

Explanation: The energy stored in a capacitor is given by the formula E = 1/2 CV^2, where C is the capacitance and V is the voltage across the capacitor. Substituting the given values, we get E = 1/2 * 2 * 10^-6 * (100)^2 = 4 J.

Which of the following materials would be the best choice for making a capacitor with a high capacitance?

a) Air

b) Glass

c) Paper

d) Aluminum foil

Answer: d) Aluminum foil

Explanation: The capacitance of a capacitor depends on the area of the plates, the distance between them, and the dielectric constant of the material between them. Aluminum foil has a high surface area and can be rolled up to form a capacitor with a large area. It is also a good conductor, which is important for minimizing resistance and maximizing capacitance.

A capacitor is connected in series with a resistor and a battery. What happens to the voltage across the capacitor as time passes?

a) It decreases exponentially.

b) It increases linearly.

c) It remains constant.

d) It oscillates.

Answer: a) It decreases exponentially.

Explanation: In a series circuit, the same current flows through all the components, so the voltage across the capacitor and the resistor must add up to the voltage of the battery. As the capacitor charges up, the voltage across it increases, but the voltage across the resistor decreases. The rate of change of the voltage across the capacitor is proportional to the current flowing through the circuit and the capacitance of the capacitor. This leads to an exponential decrease in the voltage across the capacitor as it charges up.

What is the time constant of a circuit consisting of a 10 microfarad capacitor and a 1 kilohm resistor?

a) 1 microsecond

b) 10 microseconds

c) 100 microseconds

d) 1 millisecond

Answer: b) 10 microseconds

Explanation: The time constant of an RC circuit is equal to the product of the resistance and the capacitance, ? = RC. Substituting the given values, we get ? = 10 * 10^-6 * 10^3 = 10 * 10^-3 = 10 microseconds.

A capacitor is charged up to a voltage of 12 V and then disconnected from the battery. If the capacitance is 2 microfarads, how much charge is stored on the capacitor?

a) 6 microcoulombs

b) 12 microcoulombs

c) 24 microcoulombs

d) 48 microcoulombs

Answer: b) 12 microcoulombs

Explanation: The charge stored on a capacitor is given by the formula Q = CV, where C is the capacitance and V is the voltage across the capacitor. Substituting the given values, we get Q = 2 * 10^-6 * 12 = 24 * 10^-6 = 12 microcoulombs.

Which of the following is true about the current in a capacitor?

a) The current is always zero.

b) The current is always positive.

c) The current can be positive or negative.

d) The current is independent of the voltage across the capacitor.

Answer: a) The current is always zero.

Explanation: In a DC circuit, a capacitor acts as an open circuit, so

What is the definition of capacitance?

Answer: Capacitance is the ability of a capacitor to store electric charge per unit voltage.

Define the time constant of a capacitor.

Answer: The time constant of a capacitor is the time taken by the capacitor to discharge to 63.2% of its initial charge or voltage.

What is the energy stored in a capacitor?

Answer: The energy stored in a capacitor is given by the formula: E = 1/2 CV^2, where E is the energy stored, C is the capacitance, and V is the voltage across the capacitor.

What happens when a capacitor is connected in series with a resistor and a battery?

Answer: A capacitor connected in series with a resistor and a battery forms a simple RC circuit, where the capacitor charges and discharges through the resistor.

Define the current in a capacitor.

Answer: The current in a capacitor is the rate of change of charge stored in the capacitor with respect to time.

What is the unit of capacitance?

Answer: The unit of capacitance is farad (F).

How can you increase the capacitance of a capacitor?

Answer: The capacitance of a capacitor can be increased by increasing the area of the plates, decreasing the distance between the plates, or by using a material with a high dielectric constant between the plates.

What is the charge on a capacitor when it is fully charged?

Answer: The charge on a capacitor when it is fully charged is equal to the product of its capacitance and the voltage across it.

What is the difference between a capacitor and a battery?

Answer: A capacitor stores energy in an electric field, while a battery stores energy in a chemical form.

What is the formula for the time constant of a capacitor in an RC circuit?

Answer: The formula for the time constant of a capacitor in an RC circuit is given by the product of the resistance and the capacitance, i.e., ? = RC.

Capacitors and Currents

Capacitors and Currents are an important topic in the field of physics, particularly in the study of electricity and electronics. Capacitors are devices that store electrical energy and are widely used in various electronic devices like radios, televisions, and computers. In this article, we will explore the working of capacitors and how they are used in electronic circuits, along with the concepts of currents. Capacitors: A capacitor is a device that can store electrical energy in the form of an electric field. It is made up of two parallel plates that are separated by an insulating material known as a dielectric. When a voltage is applied across the plates, an electric field is created between them, which causes the accumulation of electric charges on the plates. The amount of energy that can be stored by a capacitor is proportional to its capacitance, which is given by the formula C=Q/V, where C is the capacitance, Q is the charge stored on the plates, and V is the voltage applied across the plates. Capacitors are used in various electronic circuits to store electrical energy and to block the flow of direct current (DC) while allowing the flow of alternating current (AC). They are also used as filters to remove unwanted frequencies from a signal. Currents: In an electronic circuit, current is the flow of electric charges. There are two types of currents: direct current (DC) and alternating current (AC). In DC, the direction of flow of electric charges remains constant, whereas in AC, the direction of flow of electric charges changes periodically. The unit of current is the ampere (A), and it is given by the formula I=Q/t, where I is the current, Q is the charge, and t is the time taken for the charge to flow. Capacitors and Currents in Electronic Circuits: Capacitors are used in electronic circuits in various ways. One common application is to use a capacitor to filter out unwanted frequencies in a signal. This is achieved by connecting the capacitor in parallel with the load. Capacitors can also be used as voltage regulators in electronic circuits. This is done by using a capacitor to store energy when the voltage is high and to release energy when the voltage drops. Capacitors are also used in timing circuits, which are used in various electronic devices like clocks and timers. In a timing circuit, a capacitor is charged through a resistor and then discharged through a load. In summary, capacitors and currents are important concepts in the field of electronics. Capacitors are used to store energy, filter out unwanted frequencies, and regulate voltage in electronic circuits, while currents are used to power electronic devices. Understanding the working of capacitors and currents is essential for anyone interested in electronics and electrical engineering.