Algebra 2, 2008
51

 PAGE: 265 SET: Exercises PROBLEM: 51

In an AC circuit, the voltage E, current I, and impedance Z are related by the

Formula E = I · Z

Find the current in a circuit with voltage 14 – 8j volts and Impedance is 2 – 3j ohms.

E = I · Z

Substitute E and Z values

14 – 8j = i · (2 – 3j)

Divide each side by (2 – 3j)

Multiply the numerator and denominator by the conjugate of the denominator

2 – 3j. Conjugate of 2 3j is 2 + 3j.

(Multiply the numerator using FOIL method)  (Formula: )

Evaluate powers: .

(Multiply: )

(Multiply: )

Distribute terms using distributive property: .

(Subtract: )

(Substitute the imaginary unit value )

(Product of two same signs is positive)

Apply commutative property of addition: a + b = b + a.

(Add: 28 + 24 = 52 and 4 + 9 = 13)

(Write standard division form: )

(Divide: )

The current is 4 + 2j amps.

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