Question

Write the Kirchhoff's law of voltage and current.

Hint:

A simple way to remember the basis of each law: \begin{itemize} \item KCL (Junctions): Conservation of Charge. \item KVL (Loops): Conservation of Energy (Voltage is potential energy per unit charge). \end{itemize} Always apply a consistent sign convention when using KVL to avoid errors.

Answer 1

Gustav Kirchhoff formulated two fundamental laws that are essential for analyzing complex electrical circuits.
1. Kirchhoff's First Law (Kirchhoff's Current Law - KCL or the Junction Rule):
\begin{itemize} \item Statement: The algebraic sum of the electric currents meeting at any junction (or node) in an electrical circuit is zero. \item Mathematical Form: \[ \sum_{\text{junction}} I = 0 \] \item Explanation: This law is a direct consequence of the law of conservation of electric charge. Charge cannot be created, destroyed, or accumulated at a junction. Therefore, the total rate at which charge enters a junction must be equal to the total rate at which charge leaves it. \item Sign Convention: Currents entering a junction are typically taken as positive, while currents leaving the junction are taken as negative (or vice versa, as long as the convention is consistent). \end{itemize} 2. Kirchhoff's Second Law (Kirchhoff's Voltage Law - KVL or the Loop Rule):
\begin{itemize} \item Statement: The algebraic sum of the changes in potential (or voltage drops and EMFs) around any closed loop or mesh in an electrical circuit is zero. \item Mathematical Form: \[ \sum_{\text{closed loop}} \Delta V = 0 \] \item Explanation: This law is based on the law of conservation of energy. The electric force is a conservative force. This means that if an electric charge is moved around any closed path and returns to its starting point, the net work done on it is zero. Consequently, its net change in potential energy, and therefore electric potential, is also zero. \item Sign Convention: When traversing a loop, the potential difference across a resistor is taken as negative if moving in the direction of the current and positive if moving against it. The EMF of a source is taken as positive if moving from the negative to the positive terminal and negative if moving from positive to negative. \end{itemize}