## Related questions with answers

Question

Alternating current (AC) circuits use complex numbers to represent impedance in ohms. To find the total impedance in a circuit, you need to find the sum of the impedances from each part of the circuit. A circuit has partial impedances of 4.2 + 3i and 5 - 2.2i. What is the total impedance for the circuit?

Solution

VerifiedStep 1

1 of 2As stated, the total impedance in a circuit is the sum of the impedances from each part of the circuit. Hence, we simply add the two given partial impedances. Letting $\textbf{Z}$ be the total impedance, we have:

$\textbf{Z}=(4.2+3i)+(5-2.2i)$

$\textbf{Z}=4.2+3i+5-2.2i$

$\color{#c34632}{\textbf{Z}=9.2+0.8i\text{ ohms}}$

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