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Inductors

Inductors. Energy Storage. Current passing through a coil causes a magnetic field Energy is stored in the field Similar to the energy stored by capacitors We saw a charging time for a capacitor An inductor takes time to store energy also. Simple RL Circuit.

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Inductors

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  1. Inductors

  2. Energy Storage • Current passing through a coil causes a magnetic field • Energy is stored in the field • Similar to the energy stored by capacitors • We saw a charging time for a capacitor • An inductor takes time to store energy also

  3. Simple RL Circuit L must have units of Ohmsseconds

  4. From the Construction • Inductance N = number of turns on the coil m = permeability of the core (henrys/m) A = cross sectional area (m2) l = length of core (m) L = inductance in henrys

  5. Relative Permeability • Many texts and handbooks publish Km, where m = Kmmo mo = permeability of free space = 4p X 10-7 Wb/A • Ex: Compute L for the following coil: • N = 100 turns A = 1.3 X 10-4 m2 • l = 25 X 10-3 m Km = 400 (steel)

  6. Time Dependence , t = L/R This is the same way that voltage varied in the capacitor Try it!

  7. Notes • The final current (E/R) doesn’t depend on L • There is no voltage drop across the inductor after the full current has been established • The coil then acts as a short circuit (as if it weren’t there) • The inductance depends on the change of current (once I is established, DI/Dt → 0 and V=IR) • At first I = 0, so V = IR = 0 • As current rises the voltage drop across the resistor (IR) gets greater, leaving less voltage to be dropped through the coil.

  8. Voltage

  9. Inductors in Series Kirchhoff’s Voltage Law LT = L1 + L2 + L3

  10. Inductors in Parallel The analysis is difficult in a dc circuit since the voltage drains to zero, but the result is…

  11. Real Inductors • Inductors have… • Internal Resistance • Internal Capacitance between windings • So a real inductor in a circuit looks like…

  12. Example The equivalent circuit is

  13. Continued Comparing inductors to capacitors After about 5t, the current has reached a maximum for the coil and zero for a capacitor. The coil acts as a short, while the capacitor acts like an open circuit.

  14. Sample RLC Circuit After about 5 t, the equivalent circuit is No current flows through C1 and L1 acts as if it’s not there

  15. Solve Circuit • R1 and R2 are in series, so… • For the path ABCD IR1 + IR2 = E Notice that R2 and C1 are in parallel, so VR2 is the voltage drop across the capacitor also.

  16. Stored Energy • Capacitor • WC = ½CV2 • Inductor • WL = ½LI2

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