Electric Circuits·power-extremum-in-time-varying-circuit

Power Extremum In Time Varying Circuit

Given voltage and current as functions of time in an electrical circuit, find the time at which instantaneous power reaches its maximum value. The power is the product of voltage and current; use calculus to locate the extremum.

✓ All 2 test cases pass.

Inputs

Voltage amplitude coefficient

Multiplicative constant in the voltage expression (e.g., 80,000)

Voltage exponential decay rate

Decay constant in the exponential term of voltage (e.g., 500)

Current amplitude coefficient

Multiplicative constant in the current expression (e.g., 15)

Current exponential decay rate

Decay constant in the exponential term of current (e.g., 500)

Test cases

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#	Inputs	Expected	Got	Status
1	{"voltage_coefficient":80000,"voltage_exponent":500,"current_coefficient":15,"current_exponent":500}	0.002	0.002	✓
2	{"voltage_coefficient":100000,"voltage_exponent":1000,"current_coefficient":10,"current_exponent":1000}	0.001	0.001	✓

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Endpoint

POST/api/calculators/electric-circuits/power-extremum-in-time-varying-circuit/compute

Inputs (4)

voltage_coefficientnumberdefault 80000
voltage_exponentnumberdefault 500
current_coefficientnumberdefault 15
current_exponentnumberdefault 500

Example

curl -sX POST http://localhost:3001/api/calculators/electric-circuits/power-extremum-in-time-varying-circuit/compute \
  -H "Content-Type: application/json" \
  -d '{"inputs":{"voltage_coefficient":80000,"voltage_exponent":500,"current_coefficient":15,"current_exponent":500}}'

Try it live

Edit the body below, then click Call API.

Request body

Response

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Source: Pattern from: James W. Nilsson, Susan A. Riedel - Electric Circuits 11e - Instructor’s Solution Manual-Pearson (2019).pdf. Reproduces a standard power-extremum-in-time-varying-circuit computation; problem text paraphrased.

AI disclosure: Calculator code generated by anthropic/claude-haiku-4-5-20251001; verified by 2 test cases.