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Lecture 10 Induction Applications Chapter 20.6 20.8 Outline • Self-Inductance • RL Circuits • Energy Stored in a Magnetic Field Self-Inductance I B R Faraday’s law prevents the current in a circuit to reach the maximum value immediately. The magnetic flux through the loop increases together with the current. As a result, an induced emf appears and opposes the change in magnetic flux. The opposing emf results in a gradual increase of the current. The effect is called self-inductance. Magnitude of Self-Inductance ℇ = N B/t The self-induced emf is proportional to the time rate of change of the current. I ℇ = L t L is called inductance The SI unit of inductance is henry 1H=1Vs/A N B/t = L I / t L = N B/I = N B/I RL Circuits Solenoids or closely wrapped coils have a large inductance and are called inductors. For a circuits with a resistor ℇ IR = 0 and V= IR. Resistance is a measure of opposition to the current. Inductance is a measure of opposition to the rate of change in current (ℇ = L I / t). For a circuit with both a resistor and an inductor, the current is unable to reach its maximum value instantaneously. We can define a time constant for such a circuit as = L/R. Problem with an RL Circuit Problem: A circuit has a 10-V battery, a 5- resistor, and a 20-mH inductor. Find the circuit time constant and the current after 1 time constant. = L/R = 20 102 H / 5 = 0.04 s I = ℇ/R (1 eRt/L) t = 1 e1 = 0.632 I = 0.632 ℇ/R = 0.632 10 V / 5 = 1.26 A Energy Stored in a Magnetic Field The battery has to do work to produce a current. This work is energy stored by the inductor in its magnetic field. The energy stored by an inductor is similar to that of a capacitor. C V2 PEC = 2 L I2 PEL = 2 Summary • Self-inductance is a phenomenon of opposing to a change in current in electric circuits due to appearance of the magnetic field. • Inductor is an element with a large inductance. • Energy stored by an inductor is similar to that stored by a capacitor.