Electricity (2)

Question 1

Capacitors

Answer 1

• Capacitors store energy in circuits by storing electric charge, creating electric potential energy.
• They consist of two conductive plates separated by a dielectric, preventing charge flow.
• In a parallel plate capacitor, Q is the charge stored on the plates, and V is the potential difference across them.
• One plate holds a +Q charge, the other –Q, with a potential difference V between them.

Question 2

Capacitance

Answer 2

• Capacitance is the charge stored per unit potential difference, measured in Farads (F), often in smaller units like μF, nF, or pF.
• The capacitance equation relates capacitance C to the charge stored Q and potential difference V: C = Q / V.
• Charge stored refers to the magnitude of the charge on each plate or surface of a spherical conductor.
• Higher capacitance means a capacitor can store more charge for the same potential difference.

Question 3

Use of capacitors

Answer 3

• Energy storage: Capacitors store electric potential energy for various applications.
• Camera flashes: Provide a bright flash of light during discharge.
• Smoothing currents: Stabilize current in electronic circuits.
• Backup power: Supply power during unexpected outages for memory devices like calculators.
• Timing circuits: Used in electronic timers for precise operations.

Question 4

Charging capacitor

Answer 4

• Initial setup: A capacitor charging circuit includes a battery (e.m.f. ε), a resistor (R), a capacitor (C), and a switch, all connected in series.
• Switch closed: When the switch is closed, electrons flow from the negative terminal of the battery, through the resistor, and onto the negative plate of the capacitor.
• Plate charging begins: The positive terminal of the battery pulls electrons from one plate, leaving it positively charged, while the negative terminal pushes electrons onto the other plate, making it negatively charged.
• Insulator prevents flow: The insulator between the plates prevents charge from flowing directly between them, forcing charge to accumulate.
• Electrostatic repulsion: As negative charge builds on one plate, it increasingly repels incoming electrons, slowing the flow of charge.
• Exponential current decay: The current decreases exponentially, meaning it starts large and gradually decreases as the capacitor charges.
• Potential difference increases: The potential difference (V) across the plates rises as more charge accumulates, eventually equaling the supply voltage.
• Fully charged: The capacitor stops charging when the maximum charge is stored, determined by its capacitance (C) and the supply voltage.

Question 5

Discharging Capacitors

Answer 5

• Initial setup: A capacitor discharging circuit consists of a resistor (R), a switch, and a capacitor (C) in series. No power supply is present.
• Switch closed: When the switch is closed, the potential difference (V) across the capacitor causes a current (I) to flow through the circuit.
• Current flow: Electrons flow from the negative plate of the capacitor, through the resistor, and onto the positive plate, reducing the charge on both plates.
• Exponential decay: The current, potential difference, and charge all decrease exponentially over time. The rate of decrease is proportional to the amount remaining.
• Discharge completion: The capacitor is fully discharged when the potential difference (V) and current (I) fall to zero.
• Energy dissipation: The electrical energy stored in the capacitor is transferred to thermal energy in the resistor during discharge.
• Graphs: The current, potential difference, and charge follow an identical exponential decay pattern over time.

Question 6

Energy Stored by a Capacitor

Answer 6

• Power supply pushes electrons from the positive to the negative plate, storing electrical energy on the plates.
• Charge gradually builds up on the plates, and initially, adding more electrons to the negative plate is easy due to low repulsion.
• As the negative plate becomes more charged, repulsion increases, requiring more work to add charge.
• The charge (Q) on the capacitor is directly proportional to the potential difference (V), forming a straight-line graph.
• The electrical energy stored in the capacitor is represented by the area under the potential-charge graph, forming a triangle.

Question 7

Capacitors in Series

Answer 7

• When capacitors are connected in series, the potential difference (p.d.) is shared between them, but each capacitor stores the same charge.
• As a negative charge builds up on the left plate of capacitor C₁, an equal positive charge builds up on the right plate of C₁.
• This causes a negative charge to accumulate on the left plate of C₂, equal in size to the positive charge on the right plate of C₂.
• The charges are transferred between the plates in a way that the total charge stored across all capacitors is the same.

If V_total = V₁ + V₂
Then V_total = (Q/C₁) + (Q/C₂)

Since the current is the same through all components in a series circuit, the charge Q is the same through each capacitor and cancels out

So 1/C_total = (1/C₁) + (1/C₂)

Question 8

Capacitors in Parallel

Answer 8

• Capacitors in parallel have the same potential difference (p.d.) across them.
• Since the current is split across each junction in a parallel circuit, the charge stored on each capacitor is different.
• The total charge Q is the sum of the charges on each capacitor: Q = Q₁ + Q₂.
• The charge on each capacitor is given by Q₁ = C₁V and Q₂ = C₂ V, where V is the common p.d.
  Q_total = (C₁ + C₂) V
• The total capacitance for capacitors in parallel is C_total = C₁ + C₂ + C₃ + ….

Question 9

Time Constant

Answer 9

• The time to half (t_1/2) is the time it takes for the charge, current, or voltage of a discharging capacitor to decrease to half of its initial value.
• It is given by t_1/2 = ln(2) τ
• The time constant (τ) measures how long it takes for the charge, current, or voltage of a discharging capacitor to decrease to 37% of its original value, or for a charging capacitor to rise to 63% of its maximum value.
• τ ≈ 0.69 is a constant, and the time constant is related to resistance and capacitance by τ = 0.69RC, where R is the resistance in ohms (Ω) and C is the capacitance in farads (F).

Question 10

How to verify if potential difference (V) or charge (Q) on a capacitor decreases exponentially?

Answer 10

• Constant ratio method: Plot a** V-t graph** and check if the time constant is constant,
• when t = τ the potential difference on the capacitor will have decreased to approximately 37% of its original value
• Logarithmic graph method: Plot a graph of ln V against time (t) and check if a straight-line graph is obtained.

Question 11

Charging and Discharging graphs

Answer 11

• Charging graphs:
  
  • The shapes of the p.d. and charge against time graphs are identical
  • The current against time graph is an exponential decay curve
  • The initial value of the current starts at 0 on the y-axis and decreases exponentially
  • The initial value of the p.d. and charge starts at 0 and increases to a maximum value
• Discharge graphs:
  
  • The shape of the current, p.d., and charge against time graphs are identical
  • Each graph shows exponential decay curves with decreasing gradients
  • The initial values (I₀, V₀, and Q₀) start on the y-axis and decrease exponentially
  • The rate of discharge depends on the resistance of the circuit:
    
    • High resistance: slower discharge, current decreases, capacitor discharges more slowly
    • Low resistance: faster discharge, current increases, capacitor discharges quickly

Question 12

Electric field

Answer 12

• A region where a unit charge experiences a electrostatic force.
• Charges in the field can be attracted or repelled, depending on whether they are the same or opposite.
• The direction of the force is determined by whether the charges are opposite or like.
• Opposite charges attract, while like charges repel.

Question 13

Electric Field Lines In a uniform electric field

Answer 13

• The field lines are equally spaced at all points.
• Electric field strength is constant at all points in the field.
• The force acting on a test charge has the same magnitude and direction at all points in the field.
• Electric field between two parallel plates:
  
  • When a potential difference is applied between two parallel plates, they become charged.
  • The electric field between the plates is uniform.
  • The electric field beyond the edges of the plates is non-uniform.
  • Electric field lines between the plates are directed from the positive to the negative plate.
  • A uniform electric field has equally spaced field lines.

Question 14

Electric Field Lines In a radial electric field:

Answer 14

• In a radial electric field, the field lines are equally spaced as they exit the surface of the charge, but the distance between them increases with distance.
• The electric field strength and the magnitude of the force acting on a test charge decrease with distance from the charge producing the field.
• Around a point charge, the electric field is radial and the lines are directed radially inwards (for negative charges) or radially outwards (for positive charges).
• A radial field spreads uniformly in all directions, with the field being:
  
  • Stronger where the lines are closer together.
  • Weaker where the lines are further apart.

Question 15

Electric Field Strength

Answer 15

• The electric field strength at a point is defined as the electrostatic force per unit positive charge acting on the charge at that point.
• Electric field strength is a vector quantity and is always directed:
  
  • Away from a positive charge.
  • Towards a negative charge.

Question 16

Coulomb’s Law

Answer 16

• All charged particles produce an electric field around them, exerting a force on other charged particles within range.
• Coulomb’s Law: The force between two charges is proportional to the product of their charges and inversely proportional to the square of their separation.
• ε0 is the permittivity of free space.
• Like charges: Qq and F are positive, causing repulsion.
• Opposite charges: Qq and F are negative, causing attraction.

Question 17

Electric Field strength of a Point Charge

Answer 17

• Electric field strength in a radial field decreases with distance, following an inverse square law (1/r²) and its direction aligns with the field lines: towards a negative charge or away from a positive charge.
• A charged sphere produces a radial field and behaves like a point charge.

Question 18

Electric Field Strength in a Uniform Field

Answer 18

• Electric field strength in a uniform field between two charged plates is defined as: E = V/d, where V is the potential difference and d is the distance between the plates.
• Key points:
  
  • A greater voltage (V) results in a stronger field (E).
  • A greater separation (d) results in a weaker field (E).
  • This equation does not apply to a radial field around a point charge.
  • The field direction is from the positive to the negative plate.
• Derivation:
  
  • Work done, W, on a charge Q across a potential difference ΔV is given by:
    W = ΔV × Q
  • Work done is also defined as W = F × d, where F is force and d is distance.
  • Equating the two expressions: F × d = ΔV × Q.
  • Rearranging gives: F/Q = ΔV/d.
  • Since E = F/Q, E = ΔV/d.

Question 19

Relative permittivity

Answer 19

• Permittivity measures how easy it is to generate an electric field in a material.
• Relative permittivity (εr), or dielectric constant, is the ratio of the permittivity of a material to the permittivity of free space (ε0):
  εr = ε/ε0.
• Relative permittivity is dimensionless as it is a ratio of two quantities with the same unit.

Question 20

Effect of Dielectric on Capacitance

Answer 20

• Polar molecules in the dielectric align with the applied electric field, creating their own opposing electric field.
• This opposing field reduces the overall electric field, lowering the potential difference between the plates.
• Permittivity reflects how well polar molecules in the dielectric align with the applied field; higher alignment leads to higher permittivity.
• A parallel plate capacitor has plates of area A, separated by distance d, with a dielectric of permittivity ε between them.
• The reduction in potential difference increases the capacitance of the plates.

Question 21

Motion of Charged Particles in an Electric Field

Answer 21

• Charged particles in an electric field experience a force, causing them to move.
• In a uniform electric field, a particle moves parallel to the field lines (either along or against the lines depending on its charge).
• A charged particle moving perpendicular to the electric field will follow a parabolic trajectory due to the constant force.
• The direction of deflection depends on the charge: positive charges deflect towards the negative plate, and negative charges deflect towards the positive plate.
• The deflection depends on mass, charge, and speed: heavier particles deflect less, while larger charges and slower particles deflect more.

Formulas:
- F = EQ
- W = Fd
- The force increases the particle’s kinetic energy, causing it to accelerate at a constant rate in the direction of the force (Newton’s second law).
- If the particle’s velocity has a component perpendicular to the field, this component remains unchanged, and the velocity in that direction stays uniform (Newton’s first law).

Question 22

Electric Potential

Answer 22

• Electric potential at a point is the work done per unit positive charge in bringing a point test charge from infinity to the defined point.
• It is a scalar quantity (no direction) but can be positive or negative:
  
  • Positive around an isolated positive charge
  • Negative around an isolated negative charge
  • Zero at infinity.
• Work must be done to move a positive charge closer to another positive charge to overcome repulsion, and to move it away from a negative charge to overcome attraction.
• Potential energy increases when moving a charge towards a repelling charge and decreases when it moves away from an attracting charge.
• The total electric potential at a point from multiple charges is the sum of the potentials from each individual charge.

Question 23

The graph of potential V against distance r for a negative or positive charge

Answer 23

• For a positive (+) charge:
  
  • As the distance (r) from the charge decreases, the electric potential (V) increases.
  • This happens because more work must be done to overcome the repulsive force as the test charge moves closer.
  • V starts positive and increases as r decreases, eventually approaching zero as r approaches infinity.
• For a negative (−) charge:
  
  • As the distance (r) from the charge decreases, the electric potential (V) decreases.
  • This occurs because less work is required due to the attractive force, which pulls the test charge towards the source.
  • V starts negative and decreases (in magnitude) as r decreases, also approaching zero as r increases towards infinity.

Question 24

Electric Potential Energy

Answer 24

• Work is done when a charge moves through an electric field.
• Work is done when a positive charge moves against the field or a negative charge moves with the field.
• The work done is the same as the change in electric potential energy.
• When the electric potential is zero, the electric potential energy is also zero.
• The amount of work depends on the distance the charge moves in the field.
• q is the charge being moved, while Q is the charge producing the potential; ensure not to confuse the two when using them in calculations.

Question 25

Force-Distance Graph for a Point Charge

Answer 25

• Force (F) values are all positive.
• As r increases, F follows a 1/r² relation (inverse square law).
• The area under the graph represents work done (ΔW).
• The graph shows a steep decline as r increases.
• To estimate the area under the graph, use methods like counting squares or summing areas of trapeziums.

Question 26

Electric field between two point charges

Answer 26

• Opposite charges:
  
  • Field lines are directed from the positive charge to the negative charge.
  • As the charges get closer, the attractive force between them becomes stronger.
• Same type charges:
  
  • Field lines are directed away from two positive charges or towards two negative charges.
  • As the charges get closer, the repulsive force between them becomes stronger.
  • A neutral point exists at the midpoint where the resultant electric force is zero.

Question 27

Capacitance of an Isolated Sphere

Answer 27

• The capacitance C of a charged sphere is the charge per unit potential at the surface:
  
  • C = Q / V
• Q is the charge on the surface of a spherical conductor and can be considered as a point charge at its center.
• The potential V of an isolated point charge is given by:
  
  • V = Q / (4πε₀R)
• Combining these equations gives the capacitance of an isolated sphere:
  
  • C = 4πε₀R
• R is the radius of the sphere, and ε₀ is the permittivity of free space.

Question 28

Electric Fields vs Gravitational Fields

Answer 28

• Similarities:
  
  • Both gravitational and electrostatic forces follow the inverse square law.
  • The field lines around a point mass and a negative point charge are identical.
  • The field lines in uniform gravitational and electric fields are identical.
  • Gravitational and electric field strengths both have a 1 / r relationship in a radial field.
  • Gravitational potential and electric potential both have a 1 / r relationship.
  • Equipotential surfaces are spherical around a point mass or charge and parallel in uniform fields.
  • The work done in both fields is the product of mass and change in potential or charge and change in potential.
• Differences:
  
  • Gravitational force acts on mass, while electrostatic force acts on charge.
  • Gravitational force is always attractive, while electrostatic force can be either attractive or repulsive.
  • Gravitational potential is always negative, while electric potential can be either negative or positive.

Question 29

Magnetic Fields

Answer 29

• A magnetic field is a field of force created by either moving electric charge or permanent magnets, sometimes referred to as a B-field.
• Permanent magnets produce magnetic fields, while current-carrying wires create them due to the movement of electrons (stationary charges do not produce magnetic fields).
• Although magnetic fields are invisible, their effects can be observed through the force acting on magnetic materials, such as iron or the movement of a needle in a plotting compass.

Question 30

Field Lines in a Current-Carrying Wire

Answer 30

• Magnetic field lines around a current-carrying wire are circular rings centered on the wire.
• The field lines are strongest near the wire and weaken as they move farther away.
• Reversing the current reverses the direction of the magnetic field lines.
• The direction of the field lines can be determined using Maxwell’s right-hand screw rule:
  
  • Point your thumb in the direction of the conventional current (positive to negative).
  • The curled fingers indicate the direction of the magnetic field around the wire.

Question 31

Magnetic Field Lines in Solenoids and Coils

Answer 31

Field Lines in a Solenoid

• Electromagnets use solenoids (coils of wire) to concentrate magnetic fields.
• One end becomes the north pole, and the other becomes the south pole.
• Magnetic field lines around a solenoid resemble those of a bar magnet:
  
  • Emerge from the north pole.
  • Return to the south pole.
• The north and south poles depend on the current’s direction.
  
  • Determined using the right-hand grip rule:
    
    • Fingers follow the current direction.
    • Thumb points in the direction of the magnetic field (north to south).

.
.
.
Field Lines in a Flat Circular Coil

• A flat circular coil behaves like a single loop of a solenoid.
• Field lines:
  
  • Emerge from one side (north pole).
  • Return to the other side (south pole).
• Use the right-hand thumb rule to determine the magnetic field’s direction:
  
  • Thumb shows the magnetic field direction.
  • Fingers show the current direction.
• The magnetic fields of multiple coils in a solenoid combine to create a stronger, uniform field.

Question 32

Factors Affecting the Magnetic Field Strength

Answer 32

• The magnetic field strength of a solenoid can be increased by:
  
  • Adding a core made from a ferrous (iron-rich) material, e.g., an iron rod.
  • Adding more turns to the coil.
• When current flows through a solenoid with an iron core:
  
  • The core becomes magnetised, creating a significantly stronger field.
  • The magnetic field can strengthen by several hundred times.
• Adding more turns to the coil:
  
  • Concentrates the magnetic field lines, increasing the field strength.

Question 33

Fleming’s Left-Hand Rule

Answer 33

• Fleming’s Left-Hand Rule helps determine the direction of magnetic force on a moving charged particle in a magnetic field:
  
  • First Finger: Direction of the magnetic field.
  • Second Finger: Direction of conventional current (velocity of a moving positive charge).
  • Thumb: Direction of the magnetic force.
• Magnetic field direction in 3D is represented by:
  
  • Dots (tip of an arrow): Magnetic field coming out of the page.
  • Crosses (back of an arrow): Magnetic field going into the page.

Question 34

Magnetic Flux Density

Answer 34

• Magnetic flux density (B) is defined as the force acting per unit current per unit length on a current-carrying conductor placed perpendicular to the magnetic field.
• It is measured in tesla (T), which is defined as the magnetic flux density that produces a force of 1 N m⁻¹ on a conductor carrying a current of 1 A normal to the field.
• Magnetic flux density is also referred to as magnetic field strength.

Question 35

Force on a Current-Carrying Conductor

Answer 35

• A current-carrying conductor produces its own magnetic field.
• An external magnetic field will exert a magnetic force on the conductor.
• The maximum magnetic force is experienced when the current is perpendicular to the magnetic flux lines.
• The magnitude of the magnetic force (F) is proportional to:
  
  • Current (I)
  • Magnetic flux density (B)
  • Length of conductor in the field (L)
  • The sine of the angle (θ) between the conductor and the magnetic flux lines.
• The conductor will experience no force if the current is parallel to the magnetic field.

Question 36

Force on a Moving Charge

Answer 36

-F = BQv, where:
- F = magnetic force (N)
- B = magnetic flux density (T)
- Q = charge of the particle (C)
- v = speed of the particle (m/s)

• This is the maximum force when F, B, and v are mutually perpendicular.
• If a particle travels parallel to the magnetic field, it does not experience a magnetic force.
• When a charged particle moves at an angle θ to the magnetic field lines, the force is given by:
  F = BQv sin θ

Question 37

Motion of a Charged Particle in a Magnetic Field

Answer 37

• A charged particle in a uniform magnetic field perpendicular to its direction of motion travels in a circular path because:
  
  • The magnetic force (F) is always perpendicular to its velocity (v), causing circular motion.
  • The magnetic force always points towards the center of the circular path.
• The centripetal force provides the force required for circular motion.
• mv² / r = BQv
• Rearranging for the radius r gives:
  r = mv / BQ
• Key points from the equation:
  
  • Faster particles (v) move in larger circles: r ∝ v
  • Particles with greater mass (m) move in larger circles: r ∝ m
  • Particles with greater charge (q) move in smaller circles: r ∝ 1 / q
  • Particles in a stronger magnetic field (B) move in smaller circles: r ∝ 1 / B
• The centripetal acceleration can be calculated using Newton’s second law:
  F = ma

Question 38

Charged Particles in a Velocity Selector

Answer 38

• A velocity selector filters charged particles by using perpendicular electric and magnetic fields to allow only particles with a specific velocity to pass through.
• It is used in devices like mass spectrometers to create a beam of particles moving at the same speed.
• The selector has two oppositely charged plates creating an electric field (E) and a magnetic field (B) perpendicular to it.
• The electric force (F_E = EQ) does not depend on velocity, while the magnetic force (F_B = BQv) does. For a particle to pass through undeflected, the forces must balance: F_E = F_B.
• The selected velocity is given by the equation: v = E / B.
• Particles with velocities different from v are deflected and removed from the beam

Question 39

Magnetic Flux

Answer 39

• Magnetic flux (Φ) is the product of magnetic flux density (B) and the cross-sectional area (A) perpendicular to the magnetic field.
• It is measured in Webers (Wb).
• The flux is maximum when the magnetic field lines are perpendicular to the area.
• It is minimum when the magnetic field lines are parallel to the area.
• Magnetic flux represents the amount of magnetic field passing through a given area.

Question 40

Magnetic Flux Linkage

Answer 40

• Magnetic flux linkage is commonly used for solenoids with N turns of wire.
• It is defined as the product of the magnetic flux (Φ) and the number of turns (N) in the coil.
• The equation for flux linkage is:
  Flux linkage (ΦN) = Φ × N = B × A × N
  where:
  
  • B = magnetic flux density
  • A = cross-sectional area of the coil
  • N = number of turns in the coil
• The units of flux linkage are Weber turns (Wb turns).
• Flux linkage can also be expressed as:
  ΦN = B × A × N × cos(θ)
  where θ is the angle between the magnetic field lines and the normal to the coil.

Question 41

Faraday’s Law

Answer 41

• The magnitude of the induced e.m.f. (electromotive force) is directly proportional to the rate of change of magnetic flux linkage.
• The equation form of Faraday’s Law is:
  ε = Δ(Nɸ) / Δt
  Where:
  
  • ε = induced e.m.f (V)
  • Δ(Nɸ) = change in flux linkage (Wb turns)
  • Δt = time interval (s)

Question 42

Lenz’s Law

Answer 42

• Lenz’s Law states that the induced e.m.f. will produce effects that oppose the change causing it.
• If a north pole approaches the coil, the induced e.m.f. will create an opposing north pole to repel the incoming magnet.
• The direction of the current is determined by the right-hand grip rule:
  
  • Curl fingers around the coil in the direction of the current.
  • The thumb points along the direction of the magnetic flux, from north to south.
  • In this case, the current flows in an anti-clockwise direction, inducing a north pole to oppose the incoming magnet.

Question 43

Induced E.m.f.

Answer 43

Faraday’s Law with Lenz’s Law:

The equation that combines Faraday’s Law and Lenz’s Law is written as:
ε = - Δ(Nɸ) / Δt

• The negative sign represents Lenz’s Law.

Question 44

EMF Inducted in a Rotating Coil

Answer 44

• When a coil rotates in a uniform magnetic field, the magnetic flux through the coil changes, causing the induced e.m.f. to change.
• The e.m.f. is maximum when the coil cuts through the most magnetic field lines and zero when the coil is aligned with the field.
• The maximum e.m.f. occurs when the normal to the coil and the magnetic field is perpendicular, and the e.m.f. is zero when parallel
  • The e.m.f. can be calculated using the formula:
    ε = BANω sin(θ)
    θ = ωt
  • The e.m.f. varies sinusoidally and is 90° out of phase with the flux linkage.

Question 45

Alternators

Answer 45

• Alternator: A device that converts mechanical energy into electrical energy using a rotating coil in a magnetic field.
• Coil: A rectangular coil rotates within a uniform magnetic field, generating electricity.
• Slip Rings: The coil is connected to metal slip rings that rotate with it. These rings maintain continuous electrical contact.
• Brushes: Metal brushes press against the slip rings to transfer current to the external circuit.
• Rotation: As the coil rotates, it cuts through the magnetic field lines, inducing a potential difference (voltage) across the coil.
• Alternating Current (AC): The induced current changes direction as the coil spins, creating an alternating current.
• Meter Deflection: The pointer on the meter deflects first in one direction, then the opposite, as the current reverses.
• Reversing Direction: The induced voltage and current alternate direction continuously as the coil turns, resulting in an AC waveform.
• Continuous Rotation: This process continues as long as the coil keeps rotating, producing a steady alternating current.

Question 46

Dynamos

Answer 46

• A dynamo is a direct-current (D.C.) generator, similar to an alternator, but with a split-ring commutator instead of slip rings.
• The dynamo consists of a rotating coil in a magnetic field, and the split-ring commutator ensures that the current stays in one direction.
• In a dynamo, the induced potential difference only varies in the positive region of the graph, never reversing direction like in an alternator.
• The current in the dynamo is always positive (or negative), never alternating between positive and negative.
• As the coil rotates, it cuts through magnetic field lines, inducing a potential difference between the coil’s ends.
• The split-ring commutator changes the direction of the coil’s connection to the brushes every half turn, keeping the current leaving the dynamo in the same direction.
• This change in connection occurs each time the coil is perpendicular to the magnetic field lines.

Question 47

Transformer Basics

Answer 47

• A transformer changes high alternating voltage at low current to low alternating voltage at high current, and vice versa.
• It increases transmission efficiency by reducing heat energy loss in power lines.
• Power loss in resistors is given by P = I²R, so reducing current reduces power loss during transmission.
• Transformers are used in the National Grid to increase efficiency in power transmission.
• Step-up transformers increase voltage and decrease current for efficient transmission over long distances.
• Step-down transformers reduce voltage and increase current for local use near homes and businesses.

Question 48

Transformer Components and Functioning

Answer 48

• In a step-up transformer, the secondary coil has more turns than the primary coil, increasing voltage.
• The primary coil is powered by an alternating current (AC), creating a changing magnetic field inside the iron core.
• The changing magnetic field induces an e.m.f. in the secondary coil.
• The secondary voltage is determined by the number of coils; if there are more coils in the secondary, the voltage increases (step-up), and if there are fewer coils, the voltage decreases (step-down).
• A transformer consists of a primary coil, secondary coil, and a soft iron core.
• The soft iron core focuses and directs the magnetic field between the coils and is used because it can easily be magnetised and demagnetised.

Question 49

Eddy Currents

Answer 49

• Transformers aren’t 100% efficient, and power loss occurs due to various factors.
• The metallic core is continuously cut by the changing magnetic flux, inducing currents called eddy currents.
• Eddy currents are looping currents in the core caused by the changing magnetic flux.
• These currents:
  
  • Generate heat, leading to energy loss.
  • Create a magnetic field that opposes the field that induced them, reducing field strength.
• Reducing eddy currents:
  
  • The core is laminated, with layers separated by thin insulating material, preventing current flow.