UNIT OF INDUCTANCE
As stated before, the basic unit of inductance (L) is the HENRY (H), named after Joseph Henry, the co-discoverer with Faraday of the principle of electromagnetic induction. An inductor has an inductance of 1 henry if an emf of 1 volt is induced in the inductor when the current through the inductor is changing at the rate of 1 ampere per second. The relationship between the induced voltage, the inductance, and the rate of change of current with respect to time is stated mathematically as:
where Eind is the induced emf in volts; L is the inductance in henrys; and ΔI is the change in current in amperes occurring in Δt seconds. The symbol Δ (Greek letter delta), means "a change in ....". The henry is a large unit of inductance and is used with relatively large inductors. With small inductors, the millihenry is used. (A millihenry is equal to 1 X 10-3 henry, and one henry is equal to 1,000 millihenrys.) For still smaller inductors the unit of inductance is the microhenry (μH). (A μH = 1 X 10-6H, and one henry is equal to 1,000,000 microhenrys.)
GROWTH AND DECAY OF CURRENT IN AN LR SERIES CIRCUIT
When a battery is connected across a "pure" inductance, the current builds up to its final value at a rate determined by the battery voltage and the internal resistance of the battery. The current buildup is gradual because of the counter emf generated by the self-inductance of the coil. When the current starts to flow, the magnetic lines of force move outward from the coil. These lines cut the turns of wire on the inductor and build up a counter emf that opposes the emf of the battery. This opposition causes a delay in the time it takes the current to build up to a steady value. When the battery is disconnected, the lines of force collapse. Again these lines cut the turns of the inductor and build up an emf that tends to prolong the flow of current.
A voltage divider containing resistance and inductance may be connected in a circuit by means of a special switch, as shown in figure 2-10(A). Such a series arrangement is called an LR series circuit.
Figure 2-10. - Growth and decay of current in an LR series circuit.
When switch S1 is closed (as shown), a voltage Es appears across the voltage divider. At this instant the current will attempt to increase to its maximum value. However, this instantaneous current change causes coil L to produce a back EMF, which is opposite in polarity and almost equal to the EMF of the source. This back EMF opposes the rapid current change. Figure 2-10(B) shows that at the instant switch S1 is closed, there is no measurable growth current (ig), a minimum voltage drop is across resistor R, and maximum voltage exists across inductor L.
As current starts to flow, a voltage (eR) appears across R, and the voltage across the inductor is reduced by the same amount. The fact that the voltage across the inductor (L) is reduced means that the growth current (ig) is increased and consequently eR is increased. Figure 2-10(B)shows that the voltage across the inductor (eL) finally becomes zero when the growth current (ig) stops increasing, while the voltage across the resistor (eR) builds up to a value equal to the source voltage (ES).
Electrical inductance is like mechanical inertia, and the growth of current in an inductive circuit can be likened to the acceleration of a boat on the surface of the water. The boat does not move at the instant a constant force is applied to it. At this instant all the applied force is used to overcome the inertia of the boat. Once the inertia is overcome the boat will start to move. After a while, the speed of the boat reaches its maximum value and the applied force is used up in overcoming the friction of the water against the hull.
When the battery switch (S1) in the LR circuit of figure 2-10(A) is closed, the rate of the current increase is maximum in the inductive circuit. At this instant all the battery voltage is used in overcoming the emf of self-induction which is a maximum because the rate of change of current is maximum. Thus the battery voltage is equal to the drop across the inductor and the voltage across the resistor is zero. As time goes on more of the battery voltage appears across the resistor and less across the inductor. The rate of change of current is less and the induced emf is less. As the steady-state condition of the current is approached, the drop across the inductor approaches zero and all of the battery voltage is "dropped" across the resistance of the circuit.
Thus the voltages across the inductor and the resistor change in magnitude during the period of growth of current the same way the force applied to the boat divides itself between the effects of inertia and friction. In both examples, the force is developed first across the inertia/inductive effect and finally across the friction/resistive effect.
Figure 2 - 10(C) shows that when switch
S2 is closed (source voltage ES removed from the circuit), the flux that has been established around the inductor (L) collapses through the windings. This induces a voltage eL in the inductor that has a polarity opposite to ES and is essentially equal to ES in magnitude. The induced voltage causes decay current (id) to flow in resistor R in the same direction in which current was flowing originally (when S 1 was closed). A voltage (eR) that is initially equal to source voltage (ES) is developed across R. The voltage across the resistor (eR) rapidly falls to zero as the voltage across the inductor (eL) falls to zero due to the collapsing flux.
Just as the example of the boat was used to explain the growth of current in a circuit, it can also be used to explain the decay of current in a circuit. When the force applied to the boat is removed, the boat still continues to move through the water for a while, eventually coming to a stop. This is because energy was being stored in the inertia of the moving boat. After a period of time the friction of the water overcomes the inertia of the boat, and the boat stops moving. Just as inertia of the boat stored energy, the magnetic field of an inductor stores energy. Because of this, even when the power source is removed, the stored energy of the magnetic field of the inductor tends to keep current flowing in the circuit until the magnetic field collapse.
Q.8 When voltage is first applied to a series LR circuit, how much opposition does the inductance have to the flow of current compared to that of the circuit resistance?