Inductance and Capacitance Lecture 4

Inductance and Capacitance Inductor Relationship between voltage, current, power and energy Capacitor Relationship between voltage, current, power and energy Series-parallel combinations for inductance and capacitance

Inductor

Inductor concept An inductor consist of a coil of conducting wire. Inductance, L is the property whereby an inductor exhibits opposition to the change of current flowing through it, measured in henrys (H).

Inductance Inductance, L L = inductance in henrys (H). N = number of turns µ = core permeability A = cross-sectional area (m2) ℓ = length (m)

Inductance and Capacitance Inductor Relationship between voltage, current, power and energy Capacitor Relationship between voltage, current, power and energy Series-parallel combinations for inductance and capacitance

Relationship between voltage, current, power and energy Inductor symbol Inductor symbol Inductor Voltage Inductor Voltage

Inductor current Power

Assuming that energy is zero at time t=t 0, then inductor energy is:

Inductance and Capacitance Inductor Relationship between voltage, current, power and energy Capacitor Relationship between voltage, current, power and energy Series-parallel combinations for inductance and capacitance

CAPACITOR

Capacitor physical concept: A capacitor consists of two conducting plates separated by an insulator (or dielectric). Capacitance, C is the ratio of the charge on one plate of a capacitor to the voltage difference between the two plates, measured in farads (F).

The amount of charge stored, represented by q, is directly proportional to the applied voltage v, q = charge in coulomb (C) C = charge in farad (F) v = voltage in volt (V)

Capacitance, C: C = Capacitance in farads (F) e = permittivity of dielectric material between the plates (C2/N∙m2) A = surface area of each plates (m 2) d = distance between the plates (m)

Inductance and Capacitance Inductor Relationship between voltage, current, power and energy Capacitor Relationship between voltage, current, power and energy Series-parallel combinations for inductance and capacitance

Relationship between voltage, current, power and energy Capacitor symbol

Capacitor’scurrentCapacitor’scurrent Capacitor’s voltage

Power:

Energy stored in a capacitor from time t to t 0 :

Capacitor is not discharge at t=-∞, therefore the voltage is zero. Energy capacitor

Inductance and Capacitance Inductor Relationship between voltage, current, power and energy Capacitor Relationship between voltage, current, power and energy Series-parallel combinations for inductance and capacitance

Series and parallel capacitors The equivalent capacitance, C eq of N parallel-connected capacitors is the sum of the individual capacitances.

Using KCL,

Equivalent circuit for the parallel capacitor,

The equivalent capacitance, C eq of N series-connected capacitors is the reciprocal of the sum of the reciprocals of the individual capacitances.

Using KCL,

Equivalent circuit for the series capacitor,

Series and parallel inductors The equivalent inductance, L eq of N series-connected inductors is the sum of the individual inductances.

Using KVL,

Equivalent circuit for the series inductor,

The equivalent inductance, L eq of N parallel-connected inductors is the reciprocal of the sum of the reciprocals of the individual capacitances.

Using KVL,

Equivalent circuit for the parallel inductor,

Question 1 Obtain the total capacitance.

Answer Short circuit, then:

Question 2 Voltage stored in a 10µF capacitor is shown in figure below. Obtain the graph for current of the capacitor.

Answer Capacitor voltage: current: t tttv µsecond )( 6      tA dt tdv Cti µsecond )( )( 6 6            

Thus:

Question 3 Determine the voltage across a 2 µF capacitor if the current through it is Assume that initial capacitor voltage is zero

Answer Capacitor voltage: