Question

which resistors in the circuit must have the same amount of charge passing through each second?a. c and db. a and dc. a and bd. b and c

Explanation:

Step1: Recall the concept of current

Current \(I=\frac{Q}{t}\), where \(Q\) is charge and \(t\) is time. If the amount of charge passing through each second (\(Q/t\)) is the same, then the current \(I\) is the same. In a series - connected circuit, the current is the same through all components.

Step2: Analyze the circuit connection

Resistors \(A\) and \(D\) are in series. For resistors in series, the current \(I\) is the same. According to \(I = \frac{Q}{t}\), if \(I\) is the same and \(t = 1s\) (since we are considering charge per second), then \(Q\) (charge) is the same. Resistors \(B\) and \(C\) are in parallel (\(V_{B}=V_{C}\), \(I_{B}=\frac{V_{B}}{R_{B}}\), \(I_{C}=\frac{V_{C}}{R_{C}}\), and \(I_{B}\) and \(I_{C}\) are only equal if \(R_{B}=R_{C}\), which is not indicated). Resistors in other combinations (e.g., \(A\) and \(B\), \(C\) and \(D\)) are not in series.

Answer:

B. A and D