Physics

Charge is conserved—it can't appear or disappear at a junction. Think of current as the flow of charge per unit time: if charge flows in at rate $I_{\text{total}}$, that same charge must flow out through the three branches at rates $I_1$, $I_2$, and $I_3$. Setting inflow equal to outflow, then rearranging with a sign convention (incoming positive, outgoing negative), gives you Kirchhoff's first law in its elegant form: the sum of all currents at a node is zero.

Charge is conserved—it can't appear or disappear at a junction. Think of current as the flow of charge per unit time: if charge flows in at rate $I_{\text{total}}$, that same charge must flow out through the three branches at rates $I_1$, $I_2$, and $I_3$. Setting inflow equal to outflow, then rearranging with a sign convention (incoming positive, outgoing negative), gives you Kirchhoff's first law in its elegant form: the sum of all currents at a node is zero.