Recall Kirchhoff’s first law and understand that it is a consequence of the conservation of charge.
Kirchhoff’s First Law (Current Law)
The algebraic sum of the currents meeting at any junction (node) in an electric circuit is zero:
\$\sum{k=1}^{n} Ik = 0\$
where \$I_k\$ is the current in the \$k^{\text{th}}\$ branch, taken as positive when flowing towards the node and negative when flowing away.
Why the Law Holds – Conservation of Charge
Charge cannot accumulate at a node. If it did, the node would acquire a net charge, creating an electric field that would quickly drive charge away. Therefore, the rate at which charge enters a node must equal the rate at which it leaves:
Charge entering per unit time = \$\displaystyle\sum I_{\text{in}}\$
Charge leaving per unit time = \$\displaystyle\sum I_{\text{out}}\$
Assign a direction to each current (conventionally away from the node).
Write the algebraic sum of the currents, using the chosen sign convention.
Solve the resulting equation together with other circuit equations (e.g., Ohm’s law, Kirchhoff’s second law).
Summary Table
Statement
Mathematical Form
Physical Basis
Kirchhoff’s First Law (Current Law)
\$\displaystyle\sum{k=1}^{n} Ik = 0\$
Conservation of electric charge at a node
Kirchhoff’s Second Law (Voltage Law) – for reference
\$\displaystyle\sum{k=1}^{m} Vk = 0\$
Conservation of energy around a closed loop
Suggested diagram: A simple circuit showing a node where three branches meet, with currents \$I1\$, \$I2\$, and \$I_3\$ labeled and arrows indicating assumed directions.
Key Points to Remember
The first law is always valid, regardless of the types of elements connected to the node.
Choosing a consistent sign convention for currents is essential; the final equation will be correct even if the initial guess of direction is wrong (the solution will simply give a negative value).
Kirchhoff’s first law is a direct expression of the principle that charge cannot build up at a point in a steady‑state circuit.