P28: Electromagnetic Induction
Generators, transformers and the National Grid
Electromagnetic Induction
๐ Key Definitions
Electromagnetic induction: The process of inducing a potential difference (and current if the circuit is complete) in a conductor by moving it through a magnetic field, or by changing the magnetic field around a conductor.
Generator effect: When a wire moves through a magnetic field (or a magnetic field changes through a coil), a potential difference is induced. If the conductor is part of a complete circuit, a current flows. This is the opposite of the motor effect.
Transformer: A device that changes the voltage of an alternating current. It consists of a primary coil and a secondary coil wound on the same iron core. Transformers only work with AC.
Step-up transformer: A transformer that increases the voltage (more turns on the secondary coil than the primary).
Step-down transformer: A transformer that decreases the voltage (fewer turns on the secondary coil than the primary).
๐ Electromagnetic Induction
How Induction Happens
There are two ways to induce a potential difference:
- Moving a conductor through a magnetic field: If a wire is moved through a magnetic field (or a magnet is moved into a coil), a potential difference is induced across the ends of the conductor.
- Changing the magnetic field through a coil: If the magnetic field through a coil changes (e.g. by moving a magnet in and out), a potential difference is induced across the coil.
Key rule: The induced potential difference always opposes the change that produced it (Lenz's law). This means the induced current creates a magnetic field that tries to stop the original change — if you push a magnet into a coil, the coil's induced field repels the magnet.
Factors Affecting Induced PD
To increase the size of the induced potential difference:
- Use a stronger magnet (increase magnetic field strength)
- Move the conductor faster (rate of change of field)
- Use more turns on the coil (each turn adds its induced PD)
๐ Generators
| Property | Alternator (AC generator) | Dynamo (DC generator) |
|---|---|---|
| Output | Alternating current (AC) | Direct current (DC) |
| Connection to coil | Slip rings | Split ring commutator |
| How it works | Coil rotates in magnetic field. Slip rings maintain continuous contact, allowing the current to alternate as the coil rotates. | Coil rotates in magnetic field. Split ring commutator reverses connections every half turn, keeping current in one direction. |
| PD graph | Sinusoidal (positive and negative peaks) | Pulsating (always positive, varies from zero to maximum) |
How a generator works: A coil rotates in a magnetic field. As the coil turns, the magnetic flux through the coil changes, inducing a potential difference. When the coil is perpendicular to the field, maximum flux links the coil but the rate of change is zero (PD = 0). When the coil is parallel to the field, minimum flux links but the rate of change is maximum (PD = maximum).
๐ Transformers
Transformer equation: Vp / Vs = Np / Ns
Where:
Vp = primary voltage (V)
Vs = secondary voltage (V)
Np = number of turns on primary coil
Ns = number of turns on secondary coil
Where:
Vp = primary voltage (V)
Vs = secondary voltage (V)
Np = number of turns on primary coil
Ns = number of turns on secondary coil
For a 100% efficient transformer: Vp x Ip = Vs x Is
Where:
Ip = primary current (A)
Is = secondary current (A)
Where:
Ip = primary current (A)
Is = secondary current (A)
How Transformers Work
- An alternating current in the primary coil produces a changing magnetic field.
- The iron core carries the changing magnetic field to the secondary coil.
- The changing magnetic field through the secondary coil induces a potential difference across it (electromagnetic induction).
- If the secondary coil is part of a complete circuit, an alternating current flows.
Why transformers only work with AC: Transformers need a changing magnetic field to induce a potential difference in the secondary coil. AC produces a continuously changing magnetic field. DC produces a constant magnetic field, so no induction occurs in the secondary coil after the initial switch-on.
Transformer Types
| Transformer type | Turns relationship | Voltage relationship | Current relationship |
|---|---|---|---|
| Step-up | Ns > Np (more on secondary) | Vs > Vp (voltage increases) | Is < Ip (current decreases) |
| Step-down | Ns < Np (fewer on secondary) | Vs < Vp (voltage decreases) | Is > Ip (current increases) |
๐ญ The National Grid
The National Grid: A network of cables and transformers that connects power stations to consumers (homes, factories, etc.). It uses step-up and step-down transformers to reduce energy loss in transmission.
Why High Voltage is Used
- Power stations generate electricity at about 25,000 V.
- A step-up transformer increases this to 400,000 V for transmission across the country.
- Higher voltage means lower current (P = VI, so for the same power, higher V gives lower I).
- Lower current means less energy lost as heat in the cables (P = I2R).
- At the consumer end, step-down transformers reduce the voltage to 230 V for safe home use.
Key calculation: For a given power transmitted, doubling the voltage halves the current. Since energy loss is proportional to current squared (P = I2R), halving the current reduces energy loss to one quarter. This is why very high voltages are used for long-distance transmission.
๐งฎ Worked Examples
Example 1: Transformer turns calculation
A step-down transformer has 2000 turns on the primary coil and 100 turns on the secondary coil. The primary voltage is 230 V. Calculate the secondary voltage.
Solution:
Vp / Vs = Np / Ns
230 / Vs = 2000 / 100 = 20
Vs = 230 / 20 = 11.5 V
Example 2: Step-up transformer
A step-up transformer has 500 turns on the primary and 10,000 turns on the secondary. The input voltage is 25,000 V. Calculate the output voltage.
Solution:
Vp / Vs = Np / Ns
25000 / Vs = 500 / 10000 = 0.05
Vs = 25000 / 0.05 = 500,000 V (500 kV)
Example 3: Transformer current calculation
A 100% efficient transformer has a primary voltage of 230 V and a secondary voltage of 11.5 V. The primary current is 0.2 A. Calculate the secondary current.
Solution:
Vp x Ip = Vs x Is
230 x 0.2 = 11.5 x Is
46 = 11.5 x Is
Is = 46 / 11.5 = 4 A
Example 4: National Grid energy loss
Explain why the National Grid transmits electricity at 400,000 V rather than at 25,000 V.
Solution:
Transmitting at a higher voltage means a lower current for the same power (P = VI). Energy lost as heat in the cables depends on the current squared (P = I2R), so a lower current means much less energy is wasted as heat. Transmitting at 400,000 V instead of 25,000 V reduces the current by a factor of 16, and the power loss by a factor of 256 (16 squared).
Example 5: Finding turns ratio
A transformer converts 230 V to 46 V. The primary coil has 1150 turns. Calculate the number of turns on the secondary coil.
Solution:
Vp / Vs = Np / Ns
230 / 46 = 1150 / Ns
5 = 1150 / Ns
Ns = 1150 / 5 = 230 turns
This is a step-down transformer (fewer turns on secondary, lower voltage).
โ Practice Questions
Q1: Foundation State three ways to increase the size of an induced potential difference.
Q2: Foundation Explain the difference between an alternator and a dynamo.
Q3: Higher A transformer has 800 turns on the primary coil and 40 turns on the secondary coil. The primary voltage is 230 V. Calculate the secondary voltage.
Q4: Higher A 100% efficient step-up transformer has an input voltage of 25,000 V and an input current of 400 A. The output voltage is 400,000 V. Calculate the output current.
Q5: Foundation Explain why the National Grid uses step-up transformers between power stations and transmission cables.
Q6: Higher Explain why transformers only work with alternating current and not with direct current.
โ Answers
- Q1: Three from: use a stronger magnet, move the conductor faster through the field, use more turns of wire on the coil.
- Q2: An alternator produces alternating current (AC) and uses slip rings to connect the coil to the circuit. A dynamo produces direct current (DC) and uses a split ring commutator to reverse the connections every half turn, keeping the current flowing in one direction only.
- Q3: Vp / Vs = Np / Ns, so 230 / Vs = 800 / 40 = 20. Vs = 230 / 20 = 11.5 V
- Q4: Vp x Ip = Vs x Is. 25000 x 400 = 400000 x Is. 10,000,000 = 400000 x Is. Is = 10,000,000 / 400,000 = 25 A
- Q5: Step-up transformers increase the voltage for transmission. Higher voltage means lower current for the same power. Lower current means less energy is lost as heat in the transmission cables (since P = I2R), making the system more efficient.
- Q6: Transformers work by electromagnetic induction: the primary coil's AC produces a changing magnetic field in the iron core, which induces a potential difference in the secondary coil. With DC, the current and magnetic field are constant, so there is no changing field to induce a PD in the secondary coil (except briefly at switch-on or switch-off).
๐ฏ Exam Tips
- For electromagnetic induction, remember: movement or change is needed. A stationary wire in a constant field produces no induced PD.
- Know the difference between slip rings (alternator/AC) and split ring commutator (dynamo/DC) — this is a very common question.
- In transformer calculations, always set up the ratio Vp/Vs = Np/Ns carefully — make sure primary values are on one side and secondary on the other.
- For National Grid questions, link: high voltage → low current → less heat loss (P = I2R). Always mention the I2R equation.
- Transformers are never 100% efficient in reality — some energy is lost as heat in the coils and core. But for calculations, assume 100% efficiency unless told otherwise.
- Remember: step-up means voltage goes up and current goes down; step-down means voltage goes down and current goes up. Voltage and current change in opposite directions.
- When explaining how a transformer works, mention all four steps: AC in primary → changing magnetic field in core → induced PD in secondary → AC in secondary (if circuit complete).
๐ข Maths Skills
Mathematical Skills
Transformer calculations use two equations: Vp/Vs = Np/Ns (turns ratio) and Vp ร Ip = Vs ร Is (power conservation for 100% efficiency). Set up ratios carefully keeping primary on one side and secondary on the other. For National Grid problems, use P = IยฒR to calculate power lost in cables and P = VI to relate power, voltage and current.
Maths Example
A step-down transformer has 4000 turns on the primary coil and 200 turns on the secondary coil. The primary voltage is 23,000 V. Calculate the secondary voltage and the secondary current if the primary current is 0.5 A. Vs = Vp ร Ns/Np = 23,000 ร 200/4000 = 1150 V. Is = Vp ร Ip / Vs = 23,000 ร 0.5 / 1150 = 10 A.
โ ๏ธ Common Misconceptions
Watch Out!
1. Wrong: Transformers work with both AC and DC Correct: Transformers only work with AC โ they need a changing magnetic field to induce a potential difference in the secondary coil; DC produces a constant field so no induction occurs
2. Wrong: A step-up transformer increases both voltage and current Correct: A step-up transformer increases voltage but decreases current โ if voltage goes up, current must go down to conserve power (Vp ร Ip = Vs ร Is)
3. Wrong: Slip rings and split ring commutators do the same thing Correct: Slip rings (alternator) maintain continuous contact allowing current to alternate; split ring commutator (dynamo) reverses connections every half turn to keep current flowing in one direction
โ๏ธ 6-Mark Question
Extended Answer
6 marks: Explain why the National Grid transmits electricity at very high voltages. Describe the role of step-up and step-down transformers and explain why transmitting at high voltage reduces energy loss.
Power stations generate electricity at about 25,000 V. Before transmission across the country, a step-up transformer increases the voltage to around 400,000 V. For the same power transmitted (P = VI), a higher voltage means a lower current flows in the transmission cables. This is important because energy lost as heat in the cables depends on the current squared and the resistance (P = IยฒR). A lower current means much less energy is wasted as heat in the cables, making the transmission more efficient. For example, doubling the voltage halves the current, and since power loss depends on Iยฒ, the energy lost is reduced to one quarter. At the consumer end, step-down transformers reduce the voltage to 230 V for safe domestic use. Without the high-voltage transmission, a much larger current would flow, and far more energy would be wasted as heat, making the system very inefficient and requiring much thicker, more expensive cables.
Mark scheme: 1 mark โ step-up transformer increases voltage from 25,000 V to 400,000 V, 1 mark โ higher voltage means lower current for same power (P = VI), 1 mark โ energy loss is proportional to IยฒR, 1 mark โ lower current means much less energy wasted as heat, 1 mark โ step-down transformer reduces voltage to 230 V for safe use, 1 mark โ quantification (e.g. doubling V halves I, reducing loss by factor of 4)
๐ AO3: Analyse & Evaluate
Analysis and Evaluation
A power station generates 500 MW of power at 25,000 V. The transmission cables have a total resistance of 200 ฮฉ. Two scenarios are compared: Scenario A transmits at 25,000 V. Scenario B uses a step-up transformer to transmit at 400,000 V.
(a) Calculate the current in the cables for each scenario.
(b) Calculate the power lost in the cables for each scenario.
(c) Evaluate the benefit of using high-voltage transmission. What percentage of power is saved by using Scenario B instead of Scenario A?
Answers: (a) Scenario A: I = P/V = 500,000,000 รท 25,000 = 20,000 A. Scenario B: I = P/V = 500,000,000 รท 400,000 = 1,250 A. (b) Scenario A: P_loss = IยฒR = 20,000ยฒ ร 200 = 80,000,000,000 W = 80 GW. Scenario B: P_loss = IยฒR = 1,250ยฒ ร 200 = 312,500,000 W = 312.5 MW. (c) In Scenario A, the power loss (80 GW) far exceeds the power generated (500 MW), which is physically impossible โ the system would fail. In Scenario B, the loss is 312.5 MW out of 500 MW generated, which is 62.5% loss. This shows that even at 400,000 V, the loss is significant, but without step-up transformation the system could not function. In practice, multiple cables and lower resistances are used. The key point is that high-voltage transmission reduces IยฒR losses by a factor of (20,000/1,250)ยฒ = 256 times.
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