tsl301 - Z E max I max = s R 2 „ ωL-1 ωC 2 Current...

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RLC Series Circuit (1) Applied alternating voltage: E = E max cos ωt Resulting alternating current: I = I max cos( ωt - δ ) Goals: Find I max , δ for given E max , ω . Find voltages V R , V L , V C across devices. Loop rule: E - V R - V C - V L = 0 Note: All voltages are time-dependent. In general, all voltages have a different phase. V R has the same phase as I . ~ A V V V R C L ε V V V R C L I tsl301 – p.1/3
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RLC Series Circuit (2) Phasor diagram (for ωt = δ ): I V V V V R C L C V - L ε δ Voltage amplitudes: V R,max = I max X R = I max R V L,max = I max X L = I max ωL V C,max = I max X C = I max ωC Relation between E max and I max from geometry: E 2 max = V 2 R,max + ( V L,max - V C,max ) 2 = I 2 max " R 2 + ωL - 1 ωC « 2 # tsl302 – p.2/3
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RLC Series Circuit (3)
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Unformatted text preview: Z ≡ E max I max = s R 2 + „ ωL-1 ωC « 2 Current amplitude and phase angle: • I max = E max Z = E max q R 2 + ` ωL-1 ωC ´ 2 • tan δ = V L,max-V C,max V R,max = ωL-1 /ωC R Voltages across devices: • V R = RI = RI max cos( ωt-δ ) = V R,max cos( ωt-δ ) • V L = L dI dt =-ωLI max sin( ωt-δ ) = V L,max cos “ ωt-δ + π 2 ” • V C = 1 C Z Idt = I max ωC sin( ωt-δ ) = V C,max cos “ ωt-δ-π 2 ” I V V V V R C L C V-L ε δ tsl303 – p.3/3...
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