Determine $$ R $$ and $$ X L $$ given the following values of impedance. $$ \mathbf{Z}=\mathbf{5 3 0}+\mathrm{j} 570 \Omega $$ $$ R=\square \Omega $$ and $$ \mathrm{XL}=\square \Omega $$ $$ \mathbf{Z}=\mathbf{7 0 0}

Question

Determine $$ R $$ and $$ X L $$ given the following values of impedance. $$ \mathbf{Z}=\mathbf{5 3 0}+\mathrm{j} 570 \Omega $$ $$ R=\square \Omega $$ and $$ \mathrm{XL}=\square \Omega $$ $$ \mathbf{Z}=\mathbf{7 0 0}<\mathbf{3 0} \mathbf{0} \mathbf{\Omega} $$ $$ R=\square \Omega $$ and $$ \mathrm{XL}=\square \Omega $$

UpStudy AI · Accepted Answer

**For the impedance $$ \mathbf{Z} = 530 + j570 \, \Omega $$:**

1. The real part represents the resistance:
   $$
   R = 530 \, \Omega
   $$
2. The imaginary part represents the inductive reactance:
   $$
   X_L = 570 \, \Omega
   $$

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**For the impedance $$ \mathbf{Z} = 700 \angle 30^\circ \, \Omega $$:**

1. Write the impedance in rectangular form:
   $$
   R = Z \cos(30^\circ), \quad X_L = Z \sin(30^\circ)
   $$
2. Calculate $$ R $$:
   $$
   R = 700 \cos(30^\circ) = 700 \times \frac{\sqrt{3}}{2} \approx 700 \times 0.8660 \approx 606 \, \Omega
   $$
3. Calculate $$ X_L $$:
   $$
   X_L = 700 \sin(30^\circ) = 700 \times 0.5 = 350 \, \Omega
   $$

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**Summary:**

- For $$ \mathbf{Z} = 530 + j570 \, \Omega $$:
  $$
  R = 530 \, \Omega, \quad X_L = 570 \, \Omega
  $$

- For $$ \mathbf{Z} = 700 \angle 30^\circ \, \Omega $$:
  $$
  R \approx 606 \, \Omega, \quad X_L \approx 350 \, \Omega
  $$
For $$ \mathbf{Z} = 530 + j570 \, \Omega $$: - $$ R = 530 \, \Omega $$ - $$ X_L = 570 \, \Omega $$ For $$ \mathbf{Z} = 700 \angle 30^\circ \, \Omega $$: - $$ R \approx 606 \, \Omega $$ - $$ X_L \approx 350 \, \Omega $$

Determine and given the following values of impedance.

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