To complete the table, we first need to understand that the relationship between Voltage (V) and Current (I) in a circuit can be described by Ohm's Law, which states:
[tex]\[ V = IR \][/tex]
Where:
- [tex]\( V \)[/tex] represents the voltage
- [tex]\( I \)[/tex] represents the current
- [tex]\( R \)[/tex] represents the resistance
Given the first three values of Voltage (V) and Current (I), we can determine the resistance [tex]\( R \)[/tex] of the circuit. Let's use the first pair of values (V = 4 volts, I = 0.4 amperes) to calculate the resistance.
Using Ohm’s Law:
[tex]\[ R = \frac{V}{I} \][/tex]
Plugging in the values:
[tex]\[ R = \frac{4 \text{ volts}}{0.4 \text{ amperes}} = 10 \text{ ohms} \][/tex]
Now that we know the resistance is 10 ohms, we can use this resistance to find the currents for the remaining voltages (16V and 20V).
1. For a voltage of 16V:
[tex]\[ I = \frac{V}{R} \][/tex]
[tex]\[ I = \frac{16 \text{ volts}}{10 \text{ ohms}} = 1.6 \text{ amperes} \][/tex]
2. For a voltage of 20V:
[tex]\[ I = \frac{V}{R} \][/tex]
[tex]\[ I = \frac{20 \text{ volts}}{10 \text{ ohms}} = 2.0 \text{ amperes} \][/tex]
Thus, the completed table is:
[tex]\[
\begin{tabular}{|l|l|l|l|l|l|}
\hline
Voltage (V) & 4 & 8 & 12 & 16 & 20 \\
\hline
Current (I) & 0.4 & 0.8 & 1.2 & 1.6 & 2.0 \\
\hline
\end{tabular}
\][/tex]
