# Calculating Z_T (total impedance)

Using a mobile device so I can't upload a picture. I need to find Z_total in a circuit. I will simplify the circuit description so that its easily pictured.

The simple circuit contains The 5<20 phasor current source ("<" representing angle here). The source is in series with a 10ohm resistor and an inductor labeled 30ohms. This is a simple single-loopb.

I've never seen this before. Normally I see diagrams with inductors as impedance values (ex: j30), or in henry's, with which I would calculate impedance with j-omega-L.

How can I find Z_total for such a circuit?

I tried just summing 10+30 =40 ohms, but that is wrong. I also considered maybe its reactance, meaning omega-L = 30, and multiplying by j to get Z_inductor, then summing that with the resistor to find Z_total, but that is also wrong.

This is on an exam review and we have the answers, but not procedures. I don't have the answer to my described circuit, as the actual circuit is more complex and contains more elements. The common problem though is all the caps and inductors are labeled as ohms, not reactance, impedance or farads/henries. Not sure how to interpret this.

I will try to log on later and attach the actual circuit.

Thanks

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## 2 Answers

When there is an inductor impedance and a resistor impedance in series the total value of the impedance is: -

$Z_{total} = \sqrt{R^2 + X_L^2}$

Where, in your example R = 10 ohms and XL is 30 ohms (reactive) making the total impedance 31.623 ohms

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Thank you. How did you know the 30ohms is reactive? It wasn't stated X_L in the diagram. –  eestack Aug 5 at 13:46
@eestack You said "an inductor labeled 30ohms" and I find it difficult to imagine it could mean anything else other than it's reactive impedance. –  Andy aka Aug 5 at 14:00
That's more properly the magnitude of the impedance. The total will be a complex number - for apparent example, 10 + 30j. –  Chris Stratton Aug 5 at 17:50

$$X_L = 2 \pi F L = 30 \Omega$$

This is the equivalent impedence of the inductor. Use that to compute the total equivalent impedence of the circuit, as described in an earlier response.

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