11_Chapter 21 HomeworkCH21 Alternating Current Circuits and Electromagnetic Waves

11_Chapter 21 HomeworkCH21 Alternating Current Circuits and Electromagnetic Waves

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Alternating Current Circuits and Electromagnetic Waves 211 (d) When the instantaneous current is a maximum ( ) max iI = , the instantaneous voltage across the resistor is 2 1.3 10 = × max , max V RR vi R IRV ∆== = max = . Again, the instantaneous voltage across a capacitor is a quarter cycle out of phase with the current. Thus, when , we must have 0 ∆= C v and () 0 CC qCv =∆ = . Then, applying Kirchhoff’s loop rule to the instantaneous voltages around the series circuit at the instant when max = gives 2 1.3 10 V ,max 0 source V ∆ + R C vv + R v = 21.23 ( )( ) 2 2 60.0 Hz 0.400 H 151 L Xf L π == = 6 11 88 2 2 60.0 Hz 3.00 10 F C X fC × 4 = ( ) 2 2 60.0 151 RLC L C ZR X X =+− = +Ω 22 884 736 = and rms rms RLC V I Z = (a) 2 07 L C LC X X X =+ − = − =
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