Fill in the missing data in the following table. Case Va( V) I( mA)

step 1 In this version we have to find the missing data in the table for each cases. So for case 1, Hep

Fill in the missing data in the following table. ...

$$ \begin{array}{l} \text { Fill in the missing data in the following table. }\\ \begin{array}{lccccc} \text { Case } & \underline{V_{a}}(\mathrm{~V}) & \underline{I}(\mathrm{~mA}) & \underline{L}_{\perp}(\mathrm{mA}) & \underline{J}_{\perp}\left(\mathrm{mA} / \mathrm{cm}^{2}\right) & \underline{A}\left(\mathrm{~cm}^{2}\right) \\ 1 & 0.65 & 0.50 & & & 2 \times 10^{-4} \\ 2 & 0.70 & & 2 \times 10^{-12} & & 1 \times 10^{-3} \\ 3 & & 0.80 & & 1 \times 10^{-7} & 1 \times 10^{-4} \\ 4 & 0.72 & 1.20 & & 2 \times 10^{-8} & \end{array} \end{array} $$

$$
\begin{array}{l}
\text { Fill in the missing data in the following table. }\\
\begin{array}{lccccc}
\text { Case } & \underline{V_{a}}(\mathrm{~V}) & \underline{I}(\mathrm{~mA}) & \underline{L}_{\perp}(\mathrm{mA}) & \underline{J}_{\perp}\left(\mathrm{mA} / \mathrm{cm}^{2}\right) & \underline{A}\left(\mathrm{~cm}^{2}\right) \\
1 & 0.65 & 0.50 & & & 2 \times 10^{-4} \\
2 & 0.70 & & 2 \times 10^{-12} & & 1 \times 10^{-3} \\
3 & & 0.80 & & 1 \times 10^{-7} & 1 \times 10^{-4} \\
4 & 0.72 & 1.20 & & 2 \times 10^{-8} &
\end{array}
\end{array}
$$

Key Concepts

Dimensional Analysis and Unit Conversion

Ensuring consistency of units is a key step in calculations involving physical quantities. In problems that combine units such as mA (milliamperes) for current and mA/cm² for current density, converting and aligning units correctly is essential to accurately compute missing values. This process of dimensional analysis not only validates the computed results but also helps prevent errors in multi-step calculations.

Proportional Reasoning and Data Extrapolation

Proportional reasoning involves understanding how varying one parameter in a relationship proportionally affects another. When some data are missing in a table, one can use known relationships—such as I = J · A—to set up proportions and solve for the unknown quantities. This method is a practical approach in experimental data analysis and the interpretation of results in physics and engineering.

Relationship Between Current and Area

The relationship between current and area is embodied in the formula I = J · A. This equation allows one to deduce one quantity if the other two are known. It is essential in problems where either the current density or the physical dimensions of a device are altered, thereby enabling the calculation of missing parameters through algebraic manipulation.

Current Density

Current density is defined as the amount of current flowing per unit area, typically expressed through the formula J = I/A. This concept is critical in fields like semiconductor device physics and electrical engineering where it connects the macroscopic current to microscopic conduction phenomena. It helps in comparing devices of different sizes or when deducing material properties based on current flow.

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