Question

1. what basic rules determine if two resistors in a series - parallel combination circuit are connected in series or in parallel?

Explanation:

In a series - parallel combination circuit, for two resistors:

• Series connection: The same current \(I\) flows through both resistors. Mathematically, if \(I_1\) is the current through resistor \(R_1\) and \(I_2\) is the current through resistor \(R_2\), then \(I_1 = I_2\). Also, the sum of the voltage drops across the two resistors (\(V_1+V_2\)) is equal to the total voltage \(V\) across the combination (\(V = V_1+V_2\), where \(V_1=I R_1\) and \(V_2 = I R_2\) for a series - connected current \(I\)).
• Parallel connection: The voltage \(V\) across both resistors is the same. If \(V_1\) is the voltage across \(R_1\) and \(V_2\) is the voltage across \(R_2\), then \(V_1=V_2\). Also, the sum of the currents through the two resistors (\(I_1 + I_2\)) is equal to the total current \(I\) entering the parallel combination (\(I=I_1 + I_2\), where \(I_1=\frac{V}{R_1}\) and \(I_2=\frac{V}{R_2}\) for a parallel - connected voltage \(V\)).

Answer:

Two resistors in a series - parallel combination circuit are in series if the same current flows through them (\(I_1 = I_2\)) and the sum of their voltage drops equals the total voltage across the combination (\(V = V_1+V_2\)). They are in parallel if the same voltage is across them (\(V_1 = V_2\)) and the sum of their currents equals the total current entering the combination (\(I=I_1 + I_2\)).