= Electrical circuit
= Electric circuit
{synonym}
An <electrical circuit> is a network of components and connections used to transport <electric charge> and exchange <energy>. <Resistors> dissipate <energy>, <capacitors> store <energy> in an <electric field>, and <inductors> store <energy> in a <magnetic field>.
A <lumped-element model> represents the circuit by branch <electric currents> and terminal <electric potential differences>. <Kirchhoff's current law> expresses charge balance at connections, while <Kirchhoff's voltage law> relates the branch voltages around loops. <University Physics Volume 2 by Samuel J. Ling and others>[Section 10.3, junction and loop rules, equations 10.4–10.5]{ref} For constant ideal components, with current entering the positive-voltage terminal,
$$
v_R=Ri_R,\qquad i_C=C\frac{dv_C}{dt},\qquad v_L=L\frac{di_L}{dt}.
$$
Combining these relations produces algebraic equations or time-dependent <differential equations>.
For example, an <RC circuit> charging an initially uncharged capacitor from a fixed <voltage source> $V_0$ obeys
$$
RC\frac{dv_C}{dt}+v_C=V_0,\qquad
v_C(t)=V_0(1-e^{-t/(RC)}).
$$
The product $RC$ is its <time constant>. This transient connects <energy> storage to the rate of the circuit's response. <University Physics Volume 2 by Samuel J. Ling and others>[Section 10.5, charging a capacitor, equations 10.8–10.10]{ref} When propagation along connections matters, a <transmission line> description can replace a single lumped model.
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