Post 2: Series Circuits

In a series circuit, the components, such as resistors, are connected end-to-end, forming a single pathway for the flow of current. In this post, we will explore the characteristics and calculations related to series circuits.

Definition:

A series circuit is a circuit configuration in which the components are connected in a sequential manner, with the same current flowing through all the elements.

Voltage Distribution:

In a series circuit, the total voltage supplied by the battery is divided among the resistors. The voltage across each resistor is additive, meaning that the sum of the voltages across each resistor is equal to the total applied voltage.

The formula to calculate the total voltage in a series circuit is:

where $V_1, V_2, V_3, ... V_n$ are the voltages across each resistor.

Current Distribution:

In a series circuit, the current through each resistor is the same. This is known as the principle of current continuity, which states that the current entering a point in a circuit is equal to the current leaving that point.

The formula to calculate the total current in a series circuit is:

where $I_1, I_2, I_3, ... I_n$ are the currents through each resistor.

Resistors in Series:

The total resistance ($R_{\text{total}}$) in a series circuit is equal to the sum of the resistances of the individual resistors:

where $R_1, R_2, R_3, ... R_n$ are the resistances of each resistor.

Example:

Let's consider a series circuit with three resistors connected to a battery.

Resistor 1 has a resistance of 10 ohms, resistor 2 has a resistance of 15 ohms, and resistor 3 has a resistance of 20 ohms.

The battery supplies a voltage of 12 volts.

To find the total resistance, we simply add the resistances of all three resistors:

The total voltage across the circuit is equal to the applied voltage:

Since the resistors are in series, the current flowing through each resistor is the same. Using Ohm's Law ($V = I \times R$), we can calculate the current through the circuit:

Therefore, in this example, the total resistance is 45 ohms, and the total current flowing through the circuit is approximately 0.267 amps.