The transformer
Section: Electricity & Magnetism | Syllabus: Cambridge AS Level Physics 9702
What is a Transformer? A transformer is a device that changes the voltage of an a.c. supply. It only works with a.c. , not d.c. FIG 4.5.24: Simple transformer Two coils of wire (primary and secondary) wound on a shared soft iron core (often C-shaped or rectangular).
Primary coil connected to a.c. input. Secondary coil connected to output/load. Core provides path for magnetic field. Transformer Construction Primary coil: Connected to the a.c. input (Np turns) Secondary coil: Connected to the output (Ns turns) Soft iron core: Links the two coils magnetically Types of Transformer Step-up: Ns > Np → Vs > Vp (increases voltage) Step-down: Ns How a Transformer Works A.c.
in primary coil creates a changing magnetic field Soft iron core carries this changing field to secondary coil Changing field through secondary coil induces an e.m.f. The induced voltage depends on the ratio of turns Why A.C.
Only? D.c. produces a constant magnetic field. Electromagnetic induction requires a changing field to induce a voltage. Only a.c. provides this continuously changing field. The Transformer Equation V_p/V_s = N_p/N_s Where: V_p = primary voltage, V_s = secondary voltage N_p = primary turns, N_s = secondary turns Example: Step-Down Transformer Question: A transformer has 1000 primary turns and 50 secondary turns.
If the input voltage is 230 V, what is the output voltage? Answer V_p/V_s = N_p/N_s 230/V_s = 1000/50 V_s = 230 × 50/1000 = 11.5 V Power and Efficiency For an ideal (100% efficient) transformer: I_p V_p = I_s V_s Power in = Power out (no energy losses) Key Relationship If voltage increases (step-up), current decreases.
If voltage decreases (step-down), current increases. Example: Current in Transformer Question: A 100% efficient transformer steps up 12 V to 240 V. If the primary current is 10 A, what is the secondary current?
Answer I_p V_p = I_s V_s 10 × 12 = I_s × 240 I_s = 120/240 = 0.5 A High-Voltage Transmission Transformers are essential for efficient electricity transmission. Why Transmit at High Voltage? Power loss in cables: P = I^2 R Power Loss Equation P_loss = I^2 R To transmit the same power at higher voltage: • Current is lower (I = P/V) • Power loss is much lower (proportional to I^2) Example: Power Loss Comparison Question: A power station transmits 100 kW.
Compare power loss when transmitting at 10 kV vs 100 kV (cable resistance = 10 Ω). Answer At 10 kV: I = P/V = 100000/10000 = 10 A P_loss = I^2R = 10^2 × 10 = 1000 W At 100 kV: I = P/V = 100000/100000 = 1 A P_loss = I^2R = 1^2 × 10 = 10 W 10× higher voltage → 100× less power loss!
The National Grid Electricity distribution uses transformers: Power station: Generates electricity at ~25 kV Step-up transformer: Increases to 400 kV for transmission Transmission lines: High voltage, low current, minimal losses Step-down transformer: Reduces to 230 V for homes Advantages of High-Voltage Transmission Lower current reduces heating in cables (P = I^2R) Less energy wasted as heat More efficient delivery of power to consumers Thinner, lighter, cheaper cables can be used
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