Across Variable vs Through Variable

Across variables:

Appears across two terminal of an element
Measured relative to a reference point
e.g. voltage

Through variables:

Value is same at both terminals of an element
e.g. current

Ohm's Law

For all components that follow Ohm's law:

V = IR

where V is voltage across a component, I is current through it, and R is resistance of the component.

Impedance vs Resistance

Impedance is used when there are energy storage elements to a component.
Resistance, a special case of impedance, can be used when there is no storage element

Kirchhoff's Laws

Current

The sum of current entering a node is 0

\sum_n I_n = 0

Voltage

The sum of voltage around a closed loop is 0

\sum_n V_n = 0

Energy Storing Elements --- Reactive Elements

When you apply a voltage to a reactive element, the reactive element will start storing energy. When the voltage is removed, it will push current until all energy is dissipated.

There are two types of Reactive Elements

Inductors

A coil of wire wound around a magnetic core, such as iron.

They have a property, inductance, with SI unit henry and symbol H.

For an inductor:

V = L\frac{\mathrm{d}I}{\mathrm{d}t}

where L is the inductance of the coil.

Energy is stored in the magnetic flux around the coil.

This creates the behaviour of trying to minimize change in current.

If you remove the voltage source and open the circuit, the inductor would have a voltage approaching infinity, causing problems if the energy stored in the inductor is high enough.

Capacitor

For a capacitor:

I = C\frac{\mathrm{d}V}{\mathrm{d}t}

Energy is stored in the form of electrostatic attraction in the adjacent plates.

Capacitors try to minimize changes in voltage.

If a capacitor is shorted, the current through the connecting wires will be extremely high, causing the wires to heat up.

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