Kirchhoff's Laws

How voltage and current behave in a circuit

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These laws govern the general behaviour of current ($I$) and voltage ($V$) in circuits.

Kirchhoff’s Current Law

The algebraic sum of currents entering and leaving a node is zero: $$ \begin{equation}\begin{aligned} I_T&=I_1+I_2+I_3\\ \end{aligned}\end{equation} $$

Kirchhoff’s Voltage Law

The algebraic sum of e.m.f.’s and p.d.’s in a loop is zero: $$ \begin{equation}\begin{aligned} E-(V_1+V_2+V_3)&=0\\ \end{aligned}\end{equation} $$

Note that there does not have to be any source of power for a loop to be analyzed in a circuit. We simply consider the total e.m.f. to be zero ($0$).

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