1.10:
Voltage Dividers
In a series connection, resistors are sequentially linked, and the same current must flow through each.
The voltage across these resistors can be expressed using Ohm's law. According to Kirchhoff's voltage law, the sum of the voltage across the resistors equals the source voltage.
As a result, the current in the circuit equals the source voltage divided by the total resistance in series.
Substituting the current expression in Ohm's law gives the voltage across each resistor.
So, the source voltage is divided proportionally among multiple resistors according to their individual resistances, which is known as the principle of 'voltage division.' A circuit that demonstrates this principle is called a voltage divider.
A combination of resistors in series can be treated as a single equivalent resistor.
The resistance of this equivalent resistor equals the sum of the resistances of the individual resistors in series.
The equivalent resistance can be generalized for any number of resistors connected in series.
Similarly, a generalized expression for voltage drop across these resistors can be written.
1.10:
Voltage Dividers
In electrical circuits, resistors can be connected in series, sequentially linked one after the other. In a series configuration, the same current flows through each resistor. Ohm's law is a fundamental principle to understand the behavior of resistors in series. It expresses the voltage across these resistors in terms of the current and resistance.
Kirchhoff's voltage law implies that the sum of the voltages across the resistors in series equals the source voltage. This means that the current in the circuit is equal to the source voltage divided by the total resistance in series. This current expression can be substituted into Ohm's law to determine the voltage across each resistor. This arrangement results in a proportional division of the source voltage among multiple resistors based on their individual resistances. This principle is known as "voltage division," a circuit that exemplifies this principle is called a "voltage divider."
A combination of resistors connected in series can be treated as a single equivalent resistor. The value of this equivalent resistor is simply the sum of the resistances of the individual resistors in series. This concept extends to any number of resistors connected in series.
The voltage drop across each resistor in a series circuit is directly proportional to its resistance. As a result, resistors with larger resistance values will experience more significant voltage drops. This principle is at the core of voltage dividers, where each resistor's voltage drop is determined by its resistance relative to the total resistance in the series.
In practice, combining resistors in series or parallel is common, often necessitating a simplified representation of the circuit. This simplification is achieved by combining two resistors at a time. The equivalent resistance of two resistors in a series is the sum of their individual resistances. This technique facilitates the analysis of complex circuits, providing engineers with a valuable tool for designing and troubleshooting electrical systems.