Alright, let's address each part of the question step-by-step.
### Part (a): Completing the table
The given table is:
[tex]\[
\begin{tabular}{|l|l|l|l|l|}
\hline
Voltage (V) & 4 & 8 & 12 & 16 \\
\hline
Current (I) & 0.4 & 0.8 & 1.2 & \ldots\\
\hline
\end{tabular}
\][/tex]
The table is already complete, and the current values for each corresponding voltage are given as follows:
[tex]\[
\begin{tabular}{|l|l|l|l|l|}
\hline
Voltage (V) & 4 & 8 & 12 & 16 \\
\hline
Current (I) & 0.4 & 0.8 & 1.2 & 1.6 \\
\hline
\end{tabular}
\][/tex]
### Part (b): Demonstrate the relationship between V and I
To determine if the relationship between Voltage (V) and Current (I) follows Ohm’s Law (which states [tex]\(V = IR\)[/tex] where [tex]\(R\)[/tex] is a constant resistance), we need to check if the ratio [tex]\( \frac{V}{I} \)[/tex] remains constant for all pairs of [tex]\( V \)[/tex] and [tex]\( I \)[/tex].
Let's calculate the resistance [tex]\( R \)[/tex] for each pair:
1. For [tex]\( V = 4 \)[/tex], [tex]\( I = 0.4 \)[/tex]:
[tex]\[ R = \frac{V}{I} = \frac{4}{0.4} = 10 \][/tex]
2. For [tex]\( V = 8 \)[/tex], [tex]\( I = 0.8 \)[/tex]:
[tex]\[ R = \frac{V}{I} = \frac{8}{0.8} = 10 \][/tex]
3. For [tex]\( V = 12 \)[/tex], [tex]\( I = 1.2 \)[/tex]:
[tex]\[ R = \frac{V}{I} = \frac{12}{1.2} = 10 \][/tex]
4. For [tex]\( V = 16 \)[/tex], [tex]\( I = 1.6 \)[/tex]:
[tex]\[ R = \frac{V}{I} = \frac{16}{1.6} = 10 \][/tex]
Since the resistance [tex]\( R \)[/tex] is the same (10 ohms) for each pair of voltage and current values, this confirms that the relationship between [tex]\( V \)[/tex] and [tex]\( I \)[/tex] is linear. This linear relationship supports Ohm’s Law, which shows that the voltage [tex]\( V \)[/tex] and current [tex]\( I \)[/tex] are directly proportional to each other with a constant resistance [tex]\( R \)[/tex].
### Conclusion
Therefore, the completed table is:
[tex]\[
\begin{tabular}{|l|l|l|l|l|}
\hline
Voltage (V) & 4 & 8 & 12 & 16 \\
\hline
Current (I) & 0.4 & 0.8 & 1.2 & 1.6 \\
\hline
\end{tabular}
\][/tex]
And the relationship between voltage and current is given by [tex]\( V = IR \)[/tex], where the resistance [tex]\( R \)[/tex] is found to be 10 ohms.
