Minimum AC Voltage

Electricity and Magnetism Level 3

In the AC circuit below, what value of m m minimizes the magnitude of the voltage at the green dot position? Assume that m m is between 0 0 and 1 1 .


The answer is 0.125.

Steven Chase by Steven Chase , 37, USA

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1 solution

Current flowing through the circuit can easily be calculated as 20 7 + 8 j \dfrac{20}{7+8j} . Voltage at the point indicated is 50 − 600 m − 380 j + 40 m j 113 \dfrac{50-600m-380j+40mj}{113} . This voltage has a minimum magnitude when m= 113 904 \dfrac{113}{904} or 0.125 approximately.

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