Understanding Series Circuits

In a series circuit, components are connected along a single path, so the same current flows through all the components.

Analyzing Statement A: Current in Series

Statement A says that the same current flows through each resistor in series. This is a fundamental property of series circuits. Since there is only one path for the current to flow, the charge carriers (electrons) must pass through every component in the circuit sequentially. Therefore, the rate of flow of charge (which is the current) is the same at all points in the series circuit.

Analyzing Statement B: Voltage Drop in Series

Statement B says that in a series circuit, the voltage drops across each resistor will be directly proportional to the capacity of the resistor. The "capacity of the resistor" refers to its resistance value. According to Ohm's Law, the voltage drop (\(V\)) across a resistor is given by the product of the current (\(I\)) flowing through it and its resistance (\(R\)). The formula is:

\(V = IR\)

In a series circuit, the current (\(I\)) is the same for all resistors. Thus, for two different resistors \(R_1\) and \(R_2\) in series, the voltage drops are \(V_1 = IR_1\) and \(V_2 = IR_2\). Since \(I\) is constant, the ratio of voltage drops is \(\frac{V_1}{V_2} = \frac{IR_1}{IR_2} = \frac{R_1}{R_2}\). This shows that the voltage drop across a resistor in a series circuit is directly proportional to its resistance.

Conclusion on Statements

Based on the analysis:

• Statement A is correct because current is uniform throughout a series circuit.
• Statement B is correct because voltage drop across a resistor in a series circuit is directly proportional to its resistance, as described by Ohm's Law (\(V=IR\)), with the current (\(I\)) being constant in a series circuit.

Therefore, both statements are correct descriptions of the properties of a series circuit.