AC Circuit Analysis: Capacitors, Inductors, and Phasors, Essays (high school) of English

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Lecture 2

AC Circuit Analysis

Capacitors and

Inductors

Unlike resistors, which dissipate energy, capacitors and inductors do not dissipate but store energy, which can be retrieved at a later time

capacitors and inductors are called storage elements.

---con’d

Capacitance is the ratio of the charge on one plate of a capacitor to the voltage difference between the two plates, measured in farads (F). 1 farad = 1 coulomb/volt. Although the capacitance C of a capacitor is the ratio of the charge q per plate to the applied voltage. it does not depend on q or v  (^) It depends on the physical dimensions of the capacitor. where A is the surface area of each plate, d is the distance between the plates, and ε is the permittivity of the dielectric material between the plates

---con’d

To obtain the current-voltage

relationship of the capacitor, we

take the derivative of both sides

• (^) The instantaneous power delivered to the capacitor and the energy stored in the capacitor are

Series and Parallel

Capacitors

In order to obtain the equivalent capacitor of N capacitors in parallel, Note that the capacitors have the same voltage across them. Applying KCL The equivalent capacitance of N parallel-connected capacitors is the sum of the individual capacitances

Series-connected N

capacitors

Note that the same current i flows (and consequently the same charge) through the capacitors. Applying KVL to the loop The equivalent capacitance of series- connected capacitors is the reciprocal of the sum of the reciprocals of the individual capacitances.

Inductors

An inductor is a passive element designed

to store energy in its magnetic field



Inductors find numerous applications like

in power supplies, transformers, radios,

TVs, radars, and electric motors



An inductor consists of a coil of

conducting wire



If current is allowed to pass through an

inductor, it is found that the voltage

across the inductor is directly proportional

to the time rate of change of the current.

10 Inductance (L) is the property whereby an inductor exhibits opposition to the change of current flowing through it, measured in henrys (H).

Power and Energy in

inductor

The energy stored can be

obtained

Series and Parallel

Inductors

Consider a series connection of N inductors The equivalent inductance of series- connected inductors is the sum of the individual inductances.

parallel inductors

The equivalent inductance of

parallel inductors is the reciprocal

of the sum of the reciprocals of

the individual inductances.

AC Circuits

Introduction:



A sinusoid is a signal that has the

form of the sine or cosine function.

 A sinusoidal current is usually

referred to as alternating current

(ac).

 Such a current reverses at regular

time intervals and has alternately

positive and negative values.

 Circuits driven by sinusoidal current,

or voltage sources are called ac

circuits 19

Sinusoids

Consider the sinusoidal voltage

Where;

Vm = is the amplitude of the sinusoid

ωt = is the argument of the sinusoid

ω = the angular frequency in radians/s