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| 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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