Class 12 Physics: Electrostatics and Current Electricity

1. What is the formula for electric charge conservation?

Q = ne

Q = mv

Q = it

Q = f/a

Electric charge conservation states that the total electric charge in an isolated system remains constant over time. The formula \( q = ne \) represents this principle, where \( q \) is the total charge, \( n \) is the number of elementary charges (such as electrons), and \( e \) is the elementary charge value (approximately \( 1.6 \times 10^{-19} \) coulombs). This equation illustrates how charge is quantized and shows that charge can neither be created nor destroyed, only transferred between objects.

Explanation

Electric charge conservation states that the total electric charge in an isolated system remains constant over time. The formula \( q = ne \) represents this principle, where \( q \) is the total charge, \( n \) is the number of elementary charges (such as electrons), and \( e \) is the elementary charge value (approximately \( 1.6 \times 10^{-19} \) coulombs). This equation illustrates how charge is quantized and shows that charge can neither be created nor destroyed, only transferred between objects.

2. What is the formula for electric current?

I = q/t

I = v/r

I = r/v

I = f/q

Electric current (i) is defined as the rate of flow of electric charge (q) over a specific time interval (t). The formula i = q/t captures this relationship, indicating that current is measured in coulombs per second, which is equivalent to amperes. This formula emphasizes that a higher charge flow in a shorter time results in a greater current. Other formulas, such as i = v/r and i = r/v, pertain to specific contexts (Ohm's Law) but do not define current in terms of charge and time directly.

Explanation

Electric current (i) is defined as the rate of flow of electric charge (q) over a specific time interval (t). The formula i = q/t captures this relationship, indicating that current is measured in coulombs per second, which is equivalent to amperes. This formula emphasizes that a higher charge flow in a shorter time results in a greater current. Other formulas, such as i = v/r and i = r/v, pertain to specific contexts (Ohm's Law) but do not define current in terms of charge and time directly.

3. What is the relationship between resistance, length, and area?

R = ρ(l/a)

R = v/i

R = q/t

R = f/q

The relationship between resistance (r), length (l), and cross-sectional area (a) is described by the formula r = ρ(l/a), where ρ represents the resistivity of the material. This equation indicates that resistance increases with the length of the conductor and decreases with a larger cross-sectional area. Essentially, longer conductors offer more opposition to the flow of electric current, while wider conductors allow more current to pass through, highlighting the geometric factors that affect electrical resistance in materials.

Explanation

The relationship between resistance (r), length (l), and cross-sectional area (a) is described by the formula r = ρ(l/a), where ρ represents the resistivity of the material. This equation indicates that resistance increases with the length of the conductor and decreases with a larger cross-sectional area. Essentially, longer conductors offer more opposition to the flow of electric current, while wider conductors allow more current to pass through, highlighting the geometric factors that affect electrical resistance in materials.

4. What does Lenz's law state about induced current?

It opposes the cause

It enhances the cause

It has no effect

It is always in the same direction

Lenz's law states that the direction of induced current in a conductor will always be such that it opposes the change in magnetic flux that produced it. This means that if the magnetic field increases, the induced current will flow in a direction that creates a magnetic field opposing the increase. Conversely, if the magnetic field decreases, the induced current will flow in a direction that tries to maintain the original magnetic field. This principle is a manifestation of the conservation of energy, ensuring that energy is not created or destroyed in electromagnetic processes.

Explanation

Lenz's law states that the direction of induced current in a conductor will always be such that it opposes the change in magnetic flux that produced it. This means that if the magnetic field increases, the induced current will flow in a direction that creates a magnetic field opposing the increase. Conversely, if the magnetic field decreases, the induced current will flow in a direction that tries to maintain the original magnetic field. This principle is a manifestation of the conservation of energy, ensuring that energy is not created or destroyed in electromagnetic processes.

5. What is the lens formula?

1/f = 1/v + 1/u

F = mv

F = ma

1/f = v/u

The lens formula, \(1/f = 1/v + 1/u\), relates the focal length (f) of a lens to the object distance (u) and the image distance (v). This equation is derived from the principles of optics and describes how light rays converge or diverge when passing through a lens. Here, \(f\) represents the distance from the lens to its focal point, while \(u\) and \(v\) represent the distances from the lens to the object and the image, respectively. This relationship is fundamental in understanding how lenses form images.

Explanation

The lens formula, \(1/f = 1/v + 1/u\), relates the focal length (f) of a lens to the object distance (u) and the image distance (v). This equation is derived from the principles of optics and describes how light rays converge or diverge when passing through a lens. Here, \(f\) represents the distance from the lens to its focal point, while \(u\) and \(v\) represent the distances from the lens to the object and the image, respectively. This relationship is fundamental in understanding how lenses form images.

6. According to Coulomb's law, the force between two charges is given by which formula?

F = k(q1 * q2 / r²)

F = ma

F = qE

F = mv²/r

Coulomb's law describes the electrostatic force between two charged objects. The formula f = k(q1 * q2 / r²) indicates that the force (f) is directly proportional to the product of the magnitudes of the two charges (q1 and q2) and inversely proportional to the square of the distance (r) between them. The constant k represents Coulomb's constant, which quantifies the strength of the electrostatic force in a vacuum. This relationship highlights how the force varies with charge and distance, fundamental concepts in electrostatics.

Explanation

Coulomb's law describes the electrostatic force between two charged objects. The formula f = k(q1 * q2 / r²) indicates that the force (f) is directly proportional to the product of the magnitudes of the two charges (q1 and q2) and inversely proportional to the square of the distance (r) between them. The constant k represents Coulomb's constant, which quantifies the strength of the electrostatic force in a vacuum. This relationship highlights how the force varies with charge and distance, fundamental concepts in electrostatics.

7. What does Ohm's law state?

V = ir

V = q/t

V = f/q

V = w/q

Ohm's law states that the voltage (v) across a conductor is directly proportional to the current (i) flowing through it, with the resistance (r) being the constant of proportionality. This relationship is fundamental in electrical engineering, illustrating how increasing current leads to increased voltage, provided the resistance remains unchanged. It is expressed mathematically as v = ir, where v represents voltage, i represents current, and r represents resistance. This law helps in understanding and calculating electrical circuits.

Explanation

Ohm's law states that the voltage (v) across a conductor is directly proportional to the current (i) flowing through it, with the resistance (r) being the constant of proportionality. This relationship is fundamental in electrical engineering, illustrating how increasing current leads to increased voltage, provided the resistance remains unchanged. It is expressed mathematically as v = ir, where v represents voltage, i represents current, and r represents resistance. This law helps in understanding and calculating electrical circuits.

8. According to Fleming's left-hand rule, what does the thumb represent?

Direction of force

Direction of current

Direction of magnetic field

Direction of voltage

Fleming's left-hand rule is a mnemonic used to determine the direction of force experienced by a current-carrying conductor in a magnetic field. In this rule, the thumb represents the direction of the force acting on the conductor, while the first finger indicates the direction of the magnetic field, and the second finger shows the direction of the electric current. This visual aid helps in understanding the relationship between these three elements in electromagnetic applications.

Explanation

Fleming's left-hand rule is a mnemonic used to determine the direction of force experienced by a current-carrying conductor in a magnetic field. In this rule, the thumb represents the direction of the force acting on the conductor, while the first finger indicates the direction of the magnetic field, and the second finger shows the direction of the electric current. This visual aid helps in understanding the relationship between these three elements in electromagnetic applications.