Series Circuits

Overview

In a series circuit, components are connected end-to-end so the same current flows through each component. Voltages add up.

Formula

$R_{total} = R_1 + R_2 + R_3 + \ldots$

Calculator

Notes

• Results are approximate and should be verified for critical applications
• Input values should be within reasonable engineering ranges

Properties of Series Circuits

The fundamental rules governing series circuits are:

• Current Rule: The current is the same through every component in the series circuit.
  $I = I_1 = I_2 = I_3 = ... = I_n$

• Voltage Rule: The total voltage supplied by the source is equal to the sum of the individual voltage drops across each component.
  $U = U_1 + U_2 + U_3 + ... + U_n$

• Resistance Rule: The total resistance of the circuit is the sum of the individual resistances of all components.
  $R_{total} = R_1 + R_2 + R_3 + ... + R_n$

Key Formulas

The relationship between voltage ($U$), current ($I$), resistance ($R$), and power ($P$) in a series circuit is defined by Ohm's Law and the power law.

From Ohm's Law, the voltage drop across a single resistor $n$ is: $U_n = I \cdot R_n$

The total resistance is the sum of all resistors: $R_{total} = \sum_{i=1}^{n} R_i$

The current in the circuit is calculated using the total voltage and total resistance: $I = \frac{U}{R_{total}}$

The total power dissipated in the circuit is: $P = U \cdot I = R_{total} \cdot I^2 = \frac{U^2}{R_{total}}$

References

• Original Source