Certainly! Let's work through this step-by-step to understand the relationship between Voltage (V) and Current (I) for the given circuit, and to complete the missing values in the table.
### Step-by-Step Solution:
1. Identify the given values:
- Voltage (V): 4V, 8V, 12V, 16V, 20V
- Current (I): 0.4A, 0.8A, 1.2A, ?, ?
2. Understand the relationship:
We assume a linear relationship between Voltage (V) and Current (I), which means [tex]\( V = I \times R \)[/tex], where [tex]\( R \)[/tex] is the resistance.
3. Calculate the resistance:
- Using the first data point (V = 4V, I = 0.4A):
[tex]\( R = \frac{V}{I} = \frac{4 \text{V}}{0.4 \text{A}} = 10 \Omega \)[/tex]
- Using the second data point (V = 8V, I = 0.8A):
[tex]\( R = \frac{V}{I} = \frac{8 \text{V}}{0.8 \text{A}} = 10 \Omega \)[/tex]
- Using the third data point (V = 12V, I = 1.2A):
[tex]\( R = \frac{V}{I} = \frac{12 \text{V}}{1.2 \text{A}} = 10 \Omega \)[/tex]
- As we can see, the resistance [tex]\( R \)[/tex] is consistent across these data points and is equal to 10 Ohms.
4. Calculate the missing current values:
- For V = 16V:
[tex]\( I = \frac{V}{R} = \frac{16 \text{V}}{10 \Omega} = 1.6 \text{A} \)[/tex]
- For V = 20V:
[tex]\( I = \frac{V}{R} = \frac{20 \text{V}}{10 \Omega} = 2.0 \text{A} \)[/tex]
5. Complete the table:
\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}
### Conclusion:
The calculated resistance [tex]\( R \)[/tex] is 10 Ohms, and the current values for the missing points are 1.6 Amps for 16V and 2.0 Amps for 20V. This completes our table and confirms that the relationship between Voltage and Current for this circuit is linear with a constant resistance of 10 Ohms.
