a capacitor has plates separated by $8.89 \times 10^{-7}\text{ m}$.

what must the area of the plates be to create a capacitance of $1.11 \times 10^{-9}\text{ f}$?

$? \times 10^{?} \text{ m}^2$

Question

a capacitor has plates separated by $8.89 \times 10^{-7}\text{ m}$.

what must the area of the plates be to create a capacitance of $1.11 \times 10^{-9}\text{ f}$?

$? \times 10^{?} \text{ m}^2$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Parallel Plate Capacitor", "Capacitance" ], "new_concepts": [], "current_concepts": [ "Parallel Plate Capacitor", "Capacitance" ] } ## Identify given parameters and formula $$ \begin{aligned} d &= 8.89 \times 10^{-7}\text{ m}\ C &= 1.11 \times 10^{-9}\text{ F}\ \varepsilon_0 &\approx 8.854 \times 10^{-12}\text{ F/m}\ C &= \frac{\varepsilon_0 A}{d} \end{aligned} $$ ## Solve for area $A$ $$ \begin{aligned} A &= \frac{C \cdot d}{\varepsilon_0}\ A &= \frac{(1.11 \times 10^{-9}\text{ F}) \cdot (8.89 \times 10^{-7}\text{ m})}{8.854 \times 10^{-12}\text{ F/m}}\ A &= \frac{9.8679 \times 10^{-16}}{8.854 \times 10^{-12}}\ A &\approx 1.1145 \times 10^{-4}\text{ m}^2 \end{aligned} $$ ## Format in scientific notation $$ A \approx 1.11 \times 10^{-4}\text{ m}^2 $$ A capacitor has plates separated by $8.89 \times 10^{-7}\text{ m}$. What must the area of the plates be to create a capacitance of $1.11 \times 10^{-9}\text{ F}$? $1.11$ $\times 10^{\text{-4}}$ $\text{m}^2$ { "subject": "Natural Science", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Natural Science", "Physics", "Parallel Plate Capacitor" ] }

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QUESTION IMAGE

Question

Explanation:

Identify given parameters and formula

Solve for area \(A\)

Format in scientific notation

Answer: