# :Chapter 7 Capacitors and Inductors 1 : Objectives :Chapter 7 Capacitors and Inductors 1 : Objectives the voltage-current relationship of ideal capacitors the voltage-current relationship of ideal inductors

the energy stored series/parallel combinations of capacitors series/parallel combinations of inductors 2 :Introduction Both the inductor and the capacitor are passive

elements that are capable of storing and .delivering finite amount of energy 3 :The Capacitors Electrical symbol and current-voltage

conventions for a .capacitor Capacitor: C Unit : Farad (F) 4

:Voltage-Current Relationships 5 :Example 7.1 Find the capacitor voltage that is associated with the current .shown graphically below

6 Practice: 7.1 Determine the current through a 100-p F capacitor if its voltage as a function of time is given by the figure 7

:Energy Storage The power delivered to a capacitor is The energy stored in its electric field is therefore And thus If we select a zero energy reference at t0

8 Example: 7.2 Find the maximum energy stored in the capacitor and the energy dissipated in the resistor over the interval 0 < t < 0.5s 9

Example: 7.2 The energy dissipated in the resistor is 10 Practice: 7.2 11

:Characteristics of an Ideal Capacitor There is no current through a capacitor if the voltage across it is not changing with time. A capacitor is therefore an open circuit to dc. A finite amount of energy can be stored in a capacitor even if the current through the capacitor is zero, such as when the voltage across it is constant. It is impossible to change the voltage across a capacitor by a finite

amount in zero time, for this requires an infinite current through the . capacitor A capacitor never dissipates energy, but only stores it. Although this is true for the mathematical model, it is not true for a physical capacitor due to .finite resistances 12

Example: Capacitor with D.C. source Compute the voltage across the capacitor 13 :The Inductor .Electrical symbol and current-voltage conventions for an inductor

Inductor symbol: L Unit : Henries (H) 14 Example: 7.4 Given the waveform of the current in a 3-H inductor as . shown, determine the inductor voltage and sketch it

15 Example: 7.5 Given the waveform of the current in a 3-H inductor as .shown, determine the inductor voltage and sketch it 16

Practice: 7.4 The current through a 0.2-H inductor is shown in the figure. Assume the passive sign convention, and find .at t equal to: (a) 0; (b) 2 ms; (c) 6 ms 17

Example: 7.6 18 :Energy Storage 19

Example: 7.7 nd the maximum energy stored in the inductor and calculate how much energy is dissipated in the resistor in the time during which he energy is being stored in and then recovered from the inductor 20

Practice: 7.7 21 Characteristics of an Ideal Inductor: There is no voltage across an inductor if the current through it is not changing with time. An inductor is therefore a short circuit to dc. A finite amount of energy can be stored in an inductor even if the

voltage across the inductor is zero, such as when the current through it is constant. It is impossible to change the current through an inductor by a finite amount in zero time. The inductor never dissipates energy, but only stores it. Although this is true for the mathematical model, it is not true for a physical inductor due to series resistances.

22 Example: 23 :Inductance Combinations

;N inductors connected in series; (b) equivalent circuit) a( 24 :Inductance Combinations ;N inductors connected in parallel

equivalent circuit for circuit in ;Special case: two inductors connected in parallel 25 :Capacitance Combinations

;N capacitors connected in series; (b) equivalent circuit) a( ;Special case: two capacitors connected in series 26 :Capacitance Combinations

)c( d( ) .N capacitors connected in parallel; (d) equivalent circuit to (c)) c( 27

Example: 7.8 .simplify the network using series/parallel combinations oThe 6 F and 3 F series capacitors are first combined into a 2 FF and 3 F and 3 F series capacitors are first combined into a 2 FF series capacitors are first combined into a 2 F and 3 F series capacitors are first combined into a 2 FF equivalent, and this capacitor is then combined with the 1 F and 3 F series capacitors are first combined into a 2 FF element with which it is in parallel to yield an equivalent capacitance of 3 F and 3 F series capacitors are first combined into a 2 FF. oIn addition, the 3 H and 2 H inductors are replaced by an equivalent

1.2 H inductor, which is then added to the 0.8 H element to give a total equivalent inductance of 2 H. 28 Practice: 7.5 29

:Note No series or parallel combinations of either the inductors or the capacitors can be made 30 :Consequences of Linearity

There will be constant-coefficient linear integrodifferential equations Example: write appropriate nodal equations for the circuit 31