| Historical Profiles|
Michael Faraday (1791–1867), an English chemist and physicist, was probably the greatest experimentalist who ever lived. Born near London, Faraday realized his boyhood dream by working with the great chemist Sir Humphry Davy at the Royal Institution, where he worked for 54 years. He made several contributions in all areas of physical science and coined such words as electrolysis, anode, and cathode. His discovery of electromagnetic induction in 1831 was a major breakthrough in engineering because it provided a way of generating electricity. The electric motor and generator operate on this principle. The unit of capacitance, the farad, was named in his honor.
Joseph Henry (1797–1878), an American physicist, discovered inductance and con- structed an electric motor. Born in Albany, New York, Henry graduated from Albany Academy and taught philosophy at Princeton University from 1832 to 1846. He was the first secretary of the Smithsonian Institution. He conducted several experiments on electromagnetism and developedpowerfulelectromagnetsthatcouldliftobjectsweighingthousandsofpounds. Interestingly, Joseph Henry discovered electromagnetic induction before Faraday but failed to publish his findings. The unit of inductance, the henry, was named after him.
| What is a Capacitor ? |
A capacitor is a passive element designed to store energy in its electric field.
A capacitor consists of two conducting plates separated by an insulator(or dielectric).
Formulas that will use in the capacitor.
The capacitor is said to store the electric charge. The amount of charge stored, represented by q, is directly proportional to the applied voltage v so that where C, the constant of proportionality, is known as the capacitance of the capacitor. The unit of capacitance is the farad (F).
This is the current-voltage relationship for a capacitor, assuming the positive sign convention.
The voltage-current where v(t0) = q(t0)/C is the voltage across the capacitor at time t0. where v(t0) = q(t0)/C is the voltage across the capacitor at time t0.
The energy stored in the capacitor.
| SERIES AND PARALLEL CAPACITORS |
| PARALLEL CAPACITORS |
We know from resistive circuits that series-parallel combination is a powerful tool for reducing circuits. This technique can be extended to series- parallel connections of capacitors, which are sometimes encountered. We desire to replace these capacitors by a single equivalent capacitor Ceq.
In order to obtain the equivalent capacitor Ceq of N capacitors in parallel, consider the circuit in Fig. 6.14(a). The equivalent circuit is in Fig. 6.14(b). Note that the capacitors have the same voltage v across them. Applying KCL to Fig. 6.14(a),
i = i1 +i2 +i3 +···+iN
where
Ceq = C1 +C2 +C3 +···+CN
| SERIES OF CAPACITORS |
We now obtain Ceq of N capacitors connected in series by compar- ing the circuit in Fig. 6.15(a) with the equivalent circuit in Fig. 6.15(b). Note that the same current i flows (and consequently the same charge) through the capacitors.
v = v1 +v2 +v3 +···+vN
where
1 / Ceq =1/ C1 +1/ C2 +1 /C3 +···+1 /CN
Note that capacitors in series combine in the same manner as resistors in parallel. For N = 2 (i.e., two capacitors in series), Eq. (6.16) becomes 1/ Ceq =1 /C1 +1 /C2
or
An inductor is a passive element designed to store energy in its magnetic field. Inductors find numerous applications in electronic and power sys- tems. They are used in power supplies, transformers, radios, TVs, radars, and electric motors. Any conductor of electric current has inductive properties and may be regarded as an inductor. But in order to enhance the inductive effect, a practical inductor is usually formed into a cylindrical coil with many turns of conducting wire.
| What is an Inductor ? |
An inductor consists of a coil of conducting wire.
An inductor is a passive element designed to store energy in its magnetic field.
Formulas that will use in the inductor.
where L is the constant of proportionality called the inductance of the inductor. The unit of inductance is the henry (H).
.
Inductance is the property where by an inductor exhibits opposition to the change of current flowing through it, measured in henrys(H).
The current-voltage relationship. where i(t0) is the total current for −∞ <t<t 0 and i(−∞) = 0. The idea of making i(−∞) = 0 is practical and reasonable, because there must be a time in the past when there was no current in the inductor.
The inductor is designed to store energy in its magnetic field. Formula for energy.
| SERIES AND PARALLEL INDUCTORS |
| SERIES OF INDUCTOR |
Now that the inductor has been added to our list of passive elements, it is necessary to extend the powerful tool of series-parallel combination. We need to know how to find the equivalent inductance of a series-connected or parallel-connected set of inductors found in practical circuits. Consider a series connection of N inductors, as shown in Fig. 6.29(a), with the equivalent circuit shown in Fig. 6.29(b). The inductors have the same current through them.
v = v1 +v2 +v3 +···+vN
where
Leq = L1 +L2 +L3 +···+LN
Inductors in series are combined in exactly the same way as resistors in series.
| PARALLEL OF INDUCTOR |
We now consider a parallel connection of N inductors, as shown in Fig. 6.30(a), with the equivalent circuit in Fig. 6.30(b). The inductors have the same voltage across them.
where
It is appropriate at this point to summarize the most important character- istics of the three basic circuit elements we have studied.
| Note from Capacitor and Inductor. |
A capacitor is an open circuit to dc.
The voltage on a capacitor cannot change abruptly.
An inductor acts like a short circuit to dc.
The current through an inductor cannot change instantaneously.
| Maximum Power Transfer |
In many practical situations, a circuit is designed to provide power to a load. While for electric utilities, minimizing power losses in the process of transmission and distribution is critical for efficiency and economic reasons, there are other applications in areas such as communications where it is desirable to maximize the power delivered to a load. We now address the problem of delivering the maximum power to a load when given a system with known internal losses. It should be noted that this will result in significant internal losses greater than or equal to the power delivered to the load. The Thevenin equivalent is useful in finding the maximum power a linear circuit can deliver to a load. We assume that we can adjust the load resistance RL. If the entire circuit is replaced by its Thevenin equivalent except for the load, as shown in Fig. 4.48, the power delivered to the load is
For a given circuit, VTh and RTh are fixed. By varying the load resistance RL, the power delivered to the load varies as sketched in Fig. 4.49. We notice from Fig. 4.49 that the power is small for small or large values of RL but maximum for some value of RL between 0 and∞. We now want to show that this maximum power occurs when RL is equal to RTh. This is known as the maximum power theorem.
To prove the maximum power transfer theorem, we differentiate p in Eq. (4.21) with respect to RL and set the result equal to zero. We obtain
The maximum power transferred is obtained by substituting Eq. (4.23) into Eq. (4.21), for
| My Learning Experience XD |
I learned that capacitor is formed from two conducting plates separated by a thin
insulating layer. If a current i flows, positive change, q, will accumulate on the upper plate. To preserve charge neutrality, a balancing negative charge will be present on the lower plate. Inductors are formed from coils of wire, often around a steel or ferrite core. An inductor and capacitor are both devices that store energy. A capacitor stores charge electrical energy on two conductors separated by some insulating material. A inductor stores energy in a magnetic field. When current flows in a wire a magnetic field is set up circling the wire. Inductors use fact by making the core of the inductor a magnetic material to enhance the magnetic field around the inductor.
