For each configuration in Figure 5.89, find the individual (not combinations of) elements (voltage sources and/or resistors) that are in series.
Understand the Problem
The problem asks to identify elements (voltage sources and/or resistors) that are in series for each of the given circuit configurations in Figure 5.89. Elements in series are connected along a single path, such that the same current flows through each element.
Answer
(a) $E_1$, $R_1$ and $E_2$, $R_4$ (b) $R_1$, $R_3$, $R_5$ and $E$, $R_2$ and $R_4$, $R_6$ (c) $E$, $R_3$ (d) $E_1$, $R_1$
Answer for screen readers
(a) $E_1$ and $R_1$; $E_2$ and $R_4$ (b) $R_1$, $R_3$, and $R_5$; $E$ and $R_2$; $R_4$ and $R_6$ (c) $E$ and $R_3$ (d) $E_1$ and $R_1$
Steps to Solve
- Analyze circuit (a)
Examine circuit (a). $E_1$ and $R_1$ are in series. Also $E_2$ and $R_4$ are in series.
- Analyze circuit (b)
Examine circuit (b). $R_1$, $R_3$, and $R_5$ are in series. $E$ and $R_2$ are in series. Also $R_4$ and $R_6$ are in series.
- Analyze circuit (c)
Examine circuit (c). $E$ and $R_3$ are in series.
- Analyze circuit (d)
Examine circuit (d). $E_1$ and $R_1$ are in series.
(a) $E_1$ and $R_1$; $E_2$ and $R_4$ (b) $R_1$, $R_3$, and $R_5$; $E$ and $R_2$; $R_4$ and $R_6$ (c) $E$ and $R_3$ (d) $E_1$ and $R_1$
More Information
Elements are in series if they are connected sequentially along a single path in a circuit. This means the same current flows through each of the series elements.
Tips
A common mistake is to consider elements in parallel as being in series. Remember that elements in series must have the same current flowing through them. Also, be careful to only identify individual elements in series, as the question specifies, not combinations of series elements.
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