Math Problem Statement

R = 100 , Zo1 = 70 , tanθ= 0.561

R = 100 , Zo1 = 70 , tanθ= 0.561

Solution

The image you uploaded contains two mathematical expressions for RinoR_{ino} and XinoX_{ino} as follows:

Rino=(R2)2Zo1tan2θ(R2)2+Zo12tan2θR_{ino} = \frac{\left(\frac{R}{2}\right)^2 Z_{o1} \tan^2 \theta}{\left(\frac{R}{2}\right)^2 + Z_{o1}^2 \tan^2 \theta}

Xino=(R2)2Zo1tanθ(R2)2+Zo12tan2θX_{ino} = \frac{\left(\frac{R}{2}\right)^2 Z_{o1} \tan \theta}{\left(\frac{R}{2}\right)^2 + Z_{o1}^2 \tan^2 \theta}

Given the values:

  • R=100R = 100
  • Zo1=70Z_{o1} = 70
  • tanθ=0.561\tan \theta = 0.561

Let's compute both RinoR_{ino} and XinoX_{ino}. I'll calculate them now.The calculated values are:

  • Rino=13.63ΩR_{ino} = 13.63 \, \Omega
  • Xino=24.29ΩX_{ino} = 24.29 \, \Omega

Would you like any further clarifications or more details on these calculations?

Here are 5 related questions you might find interesting:

  1. How does the parameter tanθ\tan \theta affect the values of RinoR_{ino} and XinoX_{ino}?
  2. What is the physical significance of the parameters RinoR_{ino} and XinoX_{ino} in a circuit context?
  3. How would changing RR or Zo1Z_{o1} affect the results for RinoR_{ino} and XinoX_{ino}?
  4. What happens when tanθ=0\tan \theta = 0, and how do RinoR_{ino} and XinoX_{ino} behave?
  5. Could you explore what happens when R=Zo1R = Z_{o1}?

Tip: Always ensure to track the units of parameters during calculations to avoid dimensional inconsistencies.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Electrical Engineering

Formulas

R_{ino} = \frac{\left(\frac{R}{2}\right)^2 Z_{o1} \tan^2 \theta}{\left(\frac{R}{2}\right)^2 + Z_{o1}^2 \tan^2 \theta}
X_{ino} = \frac{\left(\frac{R}{2}\right)^2 Z_{o1} \tan \theta}{\left(\frac{R}{2}\right)^2 + Z_{o1}^2 \tan^2 \theta}

Theorems

Ohm's Law
Trigonometric Functions

Suitable Grade Level

University-Level Electrical Engineering