13. the current through a $0.5\ \omega$ resistor is given by $i = \frac{v}{0.5} = 2v$, where $v$ is the voltage in volts and $i$ is in amps.
(a) create a table of $i$-values when $v$ is $0, 2, 4, 6, 8$, and $10$.
(b) graph this linear equation.

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Accepted Answer

{ "quality": "clear", "question_count": 1, "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", "Ohms Law Modeling" ] } ## Calculate current values for the table $$ \begin{aligned} I &= \frac{V}{0.5} = 2V \ V = 0 &\implies I = 2(0) = 0 \ V = 2 &\implies I = 2(2) = 4 \ V = 4 &\implies I = 2(4) = 8 \ V = 6 &\implies I = 2(6) = 12 \ V = 8 &\implies I = 2(8) = 16 \ V = 10 &\implies I = 2(10) = 20 \end{aligned} $$ ## Determine coordinates for graphing $$ (V, I) \in \{(0, 0), (2, 4), (4, 8), (6, 12), (8, 16), (10, 20)\} $$ (a) | $V$ (volts) | $I$ (amps) | | :---: | :---: | | 0 | 0 | | 2 | 4 | | 4 | 8 | | 6 | 12 | | 8 | 16 | | 10 | 20 | (b) The graph of the linear equation $I = 2V$ is a straight line starting at the origin $(0,0)$ and passing through the points calculated in the table, with a slope of $2$. { "elements": [ { "type": "point", "params": [[0, 0]], "properties": { "name": "(0,0)", "size": 3, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[2, 4]], "properties": { "name": "(2,4)", "size": 3, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[4, 8]], "properties": { "name": "(4,8)", "size": 3, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[6, 12]], "properties": { "name": "(6,12)", "size": 3, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[8, 16]], "properties": { "name": "(8,16)", "size": 3, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[10, 20]], "properties": { "name": "(10,20)", "size": 3, "color": "#8C55F2", "withLabel": true } }, { "type": "functiongraph", "params": [ { "js": "2*x", "latex": "I = 2V" }, 0, 11 ], "properties": { "strokeColor": "#5583F2", "strokeWidth": 2 } } ] } { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Graphing Linear Relations" ] }

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Explanation:

Calculate current values for the table

Determine coordinates for graphing

Answer:

\(V\) (volts)	\(I\) (amps)
2	4
4	8
6	12
8	16
10	20