14. the inductive reactance of a $0.1\text{ h}$ coil is given by $x_l = 0.628f$, where $f$ is the frequency in hertz and $x_l$ is in ohms.
(a) create a table of values for $x_l$ with $f$-values of $0, 2, 4, 6, 8$, and $10$.
(b) graph this linear equation.

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{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Table of Values", "Graphing Linear Equations" ], "new_concepts": [], "current_concepts": [ "Table of Values", "Graphing Linear Equations", "Linear Modeling" ] } ## Calculate inductive reactance values $$ \begin{aligned} f = 0 &\implies X_L = 0.628(0) = 0 \ f = 2 &\implies X_L = 0.628(2) = 1.256 \ f = 4 &\implies X_L = 0.628(4) = 2.512 \ f = 6 &\implies X_L = 0.628(6) = 3.768 \ f = 8 &\implies X_L = 0.628(8) = 5.024 \ f = 10 &\implies X_L = 0.628(10) = 6.28 \end{aligned} $$ ## Determine linear graph parameters $$ \begin{aligned} \text{Equation: } & X_L = 0.628f \ \text{Slope: } & m = 0.628 \ \text{Intercept: } & (0, 0) \ \text{Domain: } & f \ge 0 \end{aligned} $$ ## Question 14(a) | $f$ (Hz) | $X_L$ ($\Omega$) | | :---: | :---: | | 0 | 0 | | 2 | 1.256 | | 4 | 2.512 | | 6 | 3.768 | | 8 | 5.024 | | 10 | 6.28 | ## Question 14(b) The graph of the linear equation $X_L = 0.628f$ is a straight line starting at the origin $(0,0)$ and passing through the calculated points, such as $(10, 6.28)$, for $f \ge 0$. { "elements": [ { "type": "functiongraph", "params": [ { "js": "0.628*x", "latex": "0.628f" }, 0, 11 ], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3, "name": "X_L = 0.628f", "withLabel": true } }, { "type": "point", "params": [[0, 0]], "properties": { "name": "(0, 0)", "color": "#5583F2", "size": 3, "withLabel": true } }, { "type": "point", "params": [[10, 6.28]], "properties": { "name": "(10, 6.28)", "color": "#5583F2", "size": 3, "withLabel": true } } ], "timestamps": [0.5, 1.0] } { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Graphing Linear Equations" ] }

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Calculate inductive reactance values

Determine linear graph parameters

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Question 14(a)

Question 14(b)