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What's the value of the capacitor that makes the voltage in phase with current , and then what's the circuit current and power? voltage source with three impedances

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    \$\begingroup\$ Looks like homework without any effort on your part. Add details of what you tried and where you are stuck. \$\endgroup\$
    – Ron Beyer
    Dec 5, 2017 at 22:39
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    \$\begingroup\$ Welcome to EE.SE! This appears to be a homework question. As such, you need to show us your work so far, and explain which part of the question you're having trouble with. For future reference: Homework questions on EE.SE enjoy/suffer a special treatment. We don't provide complete answers, we only provide hints or Socratic questions, and only when you have demonstrated sufficient effort of your own. Otherwise, we would be doing you a disservice, and getting swamped by homework questions at the same time. See also here. \$\endgroup\$
    – Dave Tweed
    Dec 5, 2017 at 22:40
  • \$\begingroup\$ You will learn to match reactive impedances at resonance. \$\endgroup\$ Dec 5, 2017 at 22:53

2 Answers 2

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To find the Xc that makes the voltage in phase with the current, you have to find the equivalent impedance of that branch. Then, you can find the current through Ohm's first law. So you have to think a little with these results. If you use phasor diagram may help you to understand this phenom.

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Well, the input impedance is given by:

$$\underline{\text{Z}}_{\space\text{in}}=6,25+1,25\text{j}+\frac{1}{\frac{1}{5}+\frac{1}{5+\frac{1}{100\pi\text{C}\text{j}}}}\tag1$$

Let's say that the input voltage is a sine wave without any phase difference, so we need that:

$$\arg\left(\underline{\text{Z}}_{\space\text{in}}\right)=0\space\Longleftrightarrow\space\text{C}=\frac{1}{1000\pi}\tag2$$

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