Electricity & Magnetism · AP Physics 2
Ideal Transformer & High-Voltage Grid Transmission Loss Simulator
Key exam takeaway: Line transmission loss scales as P_loss = (P/U)²*R. Boosting voltage by factor of N reduces grid line heat loss by N² (inverse-square benefit).
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3D Simulation Stage● 60 FPS
Parameter Controls
V
turns
turns
Ω
Live Derivations & Metrics
Secondary Voltage U2
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Secondary Current I2
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Primary Current I1
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Transferred Power P
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Real-Time Formula Derivation
Governing Formula:
--Substitution:
--Regime: --
Worked Examples & Exam Question Deep Dive
Worked Problem
Problem: Ideal transformer (220V in, n1:n2 = 11:1) powers a 20V 40W bulb. Find output voltage and primary current.
Step-by-Step Derivation:
- U2 = 220*(1/11) = 20V. Output power = 40W. Ideal power balance P1 = P2 = 40W => I1 = 40/220 = 0.182A.
Worked Problem
Problem: Power plant exports 100kW over 10kV line (R=10Ω). Calculate current, transmission loss, and grid efficiency.
Step-by-Step Derivation:
- Current I = 100kW/10kV = 10A. Line loss P_loss = 10²*10 = 1000W = 1kW. Delivered power = 99kW. Efficiency = 99%.
Student Inquiry Worksheet & Practice Problems
Q1. Variant 1: In ideal transformers, does primary dictate secondary, or vice versa, for voltage vs power?
Answer Key: Voltage is dictated by primary (input U1 sets U2). Current and power are dictated by secondary load (load demand sets I1 and P1).
Q2. Variant 2: Can a transformer step up or down steady DC voltage? Why or why not?
Answer Key: Never! Transformers rely on mutual induction. Steady DC produces static magnetic flux (dΦ/dt = 0), inducing zero secondary voltage.
Q3. Variant 3: When the secondary is open circuit (no load), does the primary draw current or power?
Answer Key: In ideal models, input power is zero. Real transformers draw a tiny magnetizing idle current to maintain core flux, dissipating minor core heat.
Frequently Asked Questions & Misconceptions
Does a transformer change the frequency of AC power?
Never! Transformers alter voltage and current amplitudes only. Frequency remains strictly identical (e.g. 50Hz stays 50Hz).
With multiple secondary windings, does I1/I2 = n2/n1 still apply?
No! Single-secondary ratio formula fails. Use total power balance: P_in = P_out1 + P_out2 (U1*I1 = U2*I2 + U3*I3).
Why is Ultra-High Voltage (UHV ±1100kV) grid technology a strategic engineering marvel?
Transfers clean hydropower and solar from western regions 3,000+ km to coastal cities with minimal line loss.
Does an idle phone charger plugged into the wall consume electricity when phone is unplugged?
Yes! The internal switched transformer draws ~0.05W to 0.2W phantom power to maintain idle circuitry; unplugging prevents vampire drain and aging.