Because series circuits involve only one path through current can flow, the same current flows through each component: $$ \begin{equation}\begin{aligned} I_T=I_1=I_2=I_3\\ \end{aligned}\end{equation} $$
Kirchhoff’s Voltage Law states that the sum of voltages (potential differences and electromotive forces) in any loop in a circuit is zero. $$ \begin{equation}\begin{aligned} V_T=V_1+V_2+V_3\\ \end{aligned}\end{equation} $$
In a parallel circuit, the voltage across each branch is the same: $$ \begin{equation}\begin{aligned} V_T=V_1=V_2=V_3\\ \end{aligned}\end{equation} $$
Kirchhoff’s Current Law states that the algebraic sum of currents flowing into a node (any point in a circuit) is equal to the algebraic sum of currents leaving that node. $$ \begin{equation}\begin{aligned} I_T=I_1+I_2+I_3\\ \end{aligned}\end{equation} $$