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Impedance Matching With Transformers
19 questions By Tony R. Kuphaldt
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Question 1 of 19
Suppose you were to take a 3 kW electric heater rated for 240 VAC and connect it to a 120 VAC power source. How much power would it dissipate when connected to a voltage source equal to half its rating?
Reveal answerP = 750 W
Notes:A common mistake students make is to think that applying half the normal amount of voltage to a resistor results in half the power dissipation. This is not correct. There are many ways to disprove the assertion mathematically, and I won’t bother to list my favorite here. Discuss this with your students, and see what their reasoning is.
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Question 2 of 19
How much resistance must a heating element possess in order to dissipate 3 kW of power at 240 VAC? How much resistance must a heating element possess in order to dissipate the same amount of power (3 kW) at half the voltage (120 VAC)?
Reveal answerR240V = 19.2 Ω
R120V = 4.8 Ω
Notes:This question is an exercise in algebraic manipulation. Sure, students will be able to find an equation solving for resistance in terms of power and voltage, but for the sake of algebra practice they should be asked to derive the equation from a more common power equation, such as P = [(E2)/R].
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Question 3 of 19
Calculate all voltages and all currents in this circuit, given the component values and the number of turns in each of the transformer’s windings:
Reveal answerER = 750 V
IR = 340.9 mA
Esource = 50 V
Isource = 5.114 A
Follow-up question: given the voltage and current figures of the power source, how much impedance does it “think” it is driving?
Notes:This question checks students’ ability to relate the winding ratio to voltage and current ratios in a transformer circuit. The symbolism here is common in Europe, but not so common in the United States.
