Mutual induction

https://phys.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fphys.libretexts.org%2FBookshelves%2FUniversity_Physics%2FBook%253A_University_Physics_(OpenStax)%2FBook%253A_University_Physics_II_-_Thermodynamics_Electricity_and_Magnetism_(OpenStax)%2F14%253A_Inductance%2F14.0E%253A_14.E%253A_Inductance_(Exercise) \( \newcommand\) • • • • • • • • • • • • • • • • • • 1. Show that \(NΦ_m/I\) and \(ε/(dI/dt)\), which are both expressions for self-inductance, have the same units. 2. A 10-H inductor carries a current of 20 A. Describe how a 50-V emf can be induced across it. 3. The ignition circuit of an automobile is powered by a 12-V battery. How are we able to generate large voltages with this power source? 4. When the current through a large inductor is interrupted with a switch, an arc appears across the open terminals of the switch. Explain. 5. Does self-inductance depend on the value of the magnetic flux? Does it depend on the current through the wire? Correlate your answers with the equation \(NΦ_m=LI\). 6. Would the self-inductance of a 1.0 m long, tightly wound solenoid differ from the self-inductance per meter of an infinite, but otherwise identical, solenoid? 7. Discuss how you might determine the self-inductance per unit length of a long, straight wire. 8. The self-inductance of a coil is zero if there is no current passing through the windings. True or false? 9. How does the self-inductance per unit length near the center of a solenoid (away from the ends) com...

What is Mutual Inductance? Definition: The mutual inductance of two coils is defined as the emf induced due to the magnetic field in one coil opposes the change of current and voltage in another coil. That means the two coils are magnetically linked together due to the change in The current flowing in one coil induces the voltage in another coil due to the change in magnetic flux. The amount of magnetic flux linked with the two coils is directly proportional to the mutual inductance and current change. Mutual Inductance Theory Its theory is very simple and it can be understood by using two or more coils. It was described by an American scientist Joseph Henry in the 18th century. It is referred to as one of the properties of the coil or conductor used in the circuit. The property Oliver Heaviside introduced the term inductance in the year 1886. The property of mutual inductance is the working principle of many The main drawback of the mutual inductance is, leakage of the inductance of one coil can interrupt the operation of another coil utilizing electromagnetic induction. To reduce the leakage, electrical screening is required The positioning of two coils in the circuit decides the amount of mutual inductance that links with one to the other coil. Mutual Inductance Formula The formula of two coils is given as M= ( μ0.μr. N1. N2. A) / L N2= turns of coil 2 A= cross-sectional area in m 2 L = length of the coil in meters Unit of Mutual Inductance The unit of mutual inductance...

Definition of Mutual induction Mutual induction is a phenomenon when a coil gets induced in EMF across it due to rate of change current in adjacent coil in such a way that the Definition of Mutual Inductance Mutual Inductance is the ratio between induced emf across a coil to the rate of change of Mutual Induction Whenever there is a time varying current in a coil, the time varying flux will link with the coil itself and will cause self induced emf across the coil. This emf is viewed as a voltage drop across the coil or mutual induction and the emf induced in one coil due to time varying current flowing in any other coil is called mutually induced emf. If the first coil is also connected to the time varying source, the net emf of the first coil is the resultant of self induced and mutually induced emf. Coefficient of Mutual Induction or Mutual Inductance Let us consider one coil of 1 and another coil of 2. Now we will also consider that there is a low reluctance magnetic core which couples these both coils in such a way that entire flux created by one coil will link the other coil. That means there will be no leakage of flux in the system. Now we will apply a time varying current at coil 1 keeping the coil 2 open circuited. The voltage induced across the coil 1 will be Now we will keep the first coil open and apply time varying current in coil 2. Now the flux produced by coil 2 will link coil 1 through the magnetic core and as a result, the emf induced in the coil 1 will be...

https://phys.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fphys.libretexts.org%2FBookshelves%2FUniversity_Physics%2FBook%253A_University_Physics_(OpenStax)%2FBook%253A_University_Physics_II_-_Thermodynamics_Electricity_and_Magnetism_(OpenStax)%2F14%253A_Inductance%2F14.03%253A_Self-Inductance_and_Inductors \( \newcommand\) • • • • • • • • • • • • • Learning Objectives By the end of this section, you will be able to: • Correlate the rate of change of current to the induced emf created by that current in the same circuit • Derive the self-inductance for a cylindrical solenoid • Derive the self-inductance for a rectangular toroid Mutual inductance arises when a current in one circuit produces a changing magnetic field that induces an emf in another circuit. But can the magnetic field affect the current in the original circuit that produced the field? The answer is yes, and this is the phenomenon called self-inductance. Inductors Figure \(\PageIndex\): The familiar security gate at an airport not only detects metals, but can also indicate their approximate height above the floor. (credit: “Alexbuirds”/Wikimedia Commons) Large induced voltages are found in camera flashes. Camera flashes use a battery, two inductors that function as a transformer, and a switching system or oscillator to induce large voltages. Recall from Example \(\PageIndex Wb.\] Significance The self-inductance and flux calculated in parts (a) and (b) are typical values for coils found in contemporar...

Behaviors of Inductors wrapped around a Conductive Core Suppose we were to wrap a coil of insulated wire around a loop of ferromagnetic material and energize this coil with an Insulated winding on the ferromagnetic loop has inductive reactance, limiting AC current As an X L = 2πfL and I=E/X (or I=E/Z) For the purposes of this example, though, we need to take a more detailed look at the interactions of voltage, current, and magnetic flux in the device. Here, as in any one-source, one-load circuit, the voltage dropped across the load must equal the voltage supplied by the source, assuming zero voltage dropped along with the resistance of any connecting wires. In other words, the load (inductor coil) must produce an opposing voltage equal in magnitude to the source, in order that it may balance against the source voltage and produce an algebraic loop voltage sum of zero. From where does this opposing voltage arise? If the load were a resistor (figure above (b)), the voltage drop originates from electrical energy loss, the “friction” of charge carriers flowing through the resistance. With a perfect inductor (no resistance in the coil wire), the opposing voltage comes from another mechanism: the reaction to a changing magnetic flux in the iron core. When AC current changes, flux Φ changes. Changing flux induces a counter EMF. Relationship Between Voltage, Current and Magnetic Flux Michael Faraday discovered the mathematical relationship between magnetic flux (Φ) and induced vol...

A clamp (or tong) meter with a split core uses an instrument transformer to safely measure current levels without the necessity to connect the meter to the electrical circuit. The meter works on the principle of mutual inductance. The clamp of the meter contains a magnetic core and a coil wound around it. The conductor with the current being measured acts as a primary coil of the transformer and the clamp coil is the secondary coil. The electromotive force induced in the clamp coil is proportional to the current flowing in the conductor sensed by the secondary coil. The meter measures the voltage on the clamp coil and provides reading in the units of electric current The calculator will determine the mutual inductance M of two coupled inductors according to the following formula: where k is the coupling coefficient or coupling factor, L₁ is the Two coils with mutual inductance on a circuit diagram When the current from the external circuit through an inductor coil L₁ is increasing, it creates an increasing magnetic field around the coil, which stores energy. If the current is decreasing, the magnetic field is also decreasing. This induces a voltage across the coil in the opposite direction to the current and the stored energy returns to the circuit. If another coil L₂ is placed near the first coil, the magnetic field generated in the first coil induces a voltage in the second coil. If several coils are linked together by a common magnetic field, they are said to have mutua...

Learning Objectives By the end of this section, you will be able to: • Calculate the inductance of an inductor. • Calculate the energy stored in an inductor. • Calculate the emf generated in an inductor. Inductors Induction is the process in which an emf is induced by changing magnetic flux. Many examples have been discussed so far, some more effective than others. Transformers, for example, are designed to be particularly effective at inducing a desired voltage and current with very little loss of energy to other forms. Is there a useful physical quantity related to how “effective” a given device is? The answer is yes, and that physical quantity is called inductance. Mutual inductance is the effect of Faraday’s law of induction for one device upon another, such as the primary coil in transmitting energy to the secondary in a transformer. See Figure 23.37 These coils can induce emfs in one another like an inefficient transformer. Their mutual inductance M indicates the effectiveness of the coupling between them. Here a change in current in coil 1 is seen to induce an emf in coil 2. (Note that " E 2 E 2 induced" represents the induced emf in coil 2.) In the many cases where the geometry of the devices is fixed, flux is changed by varying current. We therefore concentrate on the rate of change of current, Δ I /Δ t Δ I /Δ t, as the cause of induction. A change in the current I 1 I 1 in one device, coil 1 in the figure, induces an emf 2 emf 2 in the other. We express this in e...