Lecture 6 Capacitor and Inductor

# without magnetic material enclosed with magnetic

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Unformatted text preview: ! ! ! ! ! !! ! !" !!! !! ! ! !! !! !"! !" !! ! ! ! !! ! !!!!" !!!! !! Capacitor (Cont.) ! ! ! ! !" !!!!! ! ! •  Assuming voltage across capacitor at t = -∞ is 0, energy ! stored in a capacitor:! !"!!! ! ! !! ! ! ! !! ! !! !! !" ! !! ! ! ! !"! !! ! !"!!! !! ! ! !!!!!"! !" !! ! ! ! !! !!!!!"!!!! !! ! ! ! ! !"!!!!! ! ! 13 Capacitor (Cont.) •  Exercise 1:A 54µF capacitor is connected to a voltage which varies in time as v(t) = 10sin(200πt) volts. Calculate the current i(t) through the capacitor. 14 Capacitor (Cont.) •  Exercise 2:- C1 V1 R1 + - F D B A + V2 - R2 R3 C E •  Calculate the energy stored in the capacitor of the circuit above under DC conditions 15 Inductor •  Another element in electric circuit •  Resistor dissipates energy •  Inductor is a coil which stores energy instead in magnetic field •  Current i(t) flows through a wire of length l and with N turns, which forms a loop of area A will create a magnetic field B(t) 16 Inductor (Cont.) Without magnetic material enclosed :- With magnetic material enclosed :- !" !!! ! ! ! !! ! ! ! !" !!! ! ! ! !! ! !! ! ! where µ0 and µr are the permeability of free space and the relative permeability of the material respectively Wire of length l i(t) B(t) Loop area A 17 ! !" !!! ! ! ! !! ! ! Inductor (Cont.) !" !!! ! ! ! !!"!! ! ! •  Magnetic flux !through the area A is expressed as:!!! !" !!! ! ! !" ! ! ! !! !! ! ! ! !! ! ! ! ! µ depending if a magnetic material is where µ = µ0 or µ0 r ! !! !!! ! !!! !" !!! ! !!! ! !"!! ! !! ! enclose...
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