Circuits | Notion

This topic is contained in pages $191-203$ of the textbook.

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Inductance (measured in $H$) is the tendency of a conductor to oppose a change in current, due to the magnetic field it produces. Self-inductance is the effect of a changing current in a coil which produces an EMF across its ends.

→ An “inductor” is normally shown as a coil of wire in a circuit.

The following relationship can be used to solve problems relating to EMF, rate of change of current ($A s^{-1}$), self-inductance (inductance) ($H$).

$$ \epsilon = -L\dfrac{dI}{dt} $$

Lenz’s law states that the direction of the induced EMF is such that it opposes the change producing it. This is an example of the principle of conservation of energy, as, if Lenz’s law were not the case, energy would be created from nothing. This produced EMF opposes the change in current (the supply voltage), so it is known as back EMF.

When the current flowing through a coil changes, this results in a changing magnetic field, inducing a back EMF on the coil itself — hence, self-inductance.

→ When a circuit is first connected, the current is rapidly increasing which produces an increasing (changing) magnetic field that results in a self-induced (back) EMF across the inductor. By Lenz’s law, this EMF opposes the change that causes it (the increasing supply EMF), resulting in the increase in current slowing down.

The graph after the switch is closed.

→ When a circuit is first disconnected, the current is rapidly decreasing which produces a decreasing (changing) magnetic field, resulting in a self-induced (back) EMF across the inductor. By Lenz’s law, this EMF opposes the change that causes it (the decreasing supply EMF), resulting in the decrease in current slowing down.

The graph after the switch is opened

Energy is stored in the magnetic field around a current-carrying inductor.

The following relationship can be used to solve problems relating to current, energy, and self-inductance (inductance).

$$ E=\dfrac{1}{2}LI^2 $$

An RC circuit contains a resistor and a capacitor, normally connected in series.

During the charging cycle of an RC circuit, as the capacitor charges, the current in the circuit decreases and the potential difference across the capacitor increases.