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# Complex numbers question

Anonymous
wrote...
A month ago
 Complex numbers question View attached fileTranscriptA capacitor of capacitance C is connected to a alternating voltage source V (t) as shown in the diagram below. c The voltage source alternatively charges and discharges the capacitor, generating an alternating Current I(t) in the wires. wires are assumed to be of negligible resistance. Complex numbers are useful in AC circuits to conveniently represent amplitudes (modulus) and phase shifts (argument). Here we assume that the source generates a voltage voe•w (1) with amplitude % and frequency co. In reality, V (t) is the real value of this complex-valued function, but all calculations can be done with complex numbers and real values taken at the end. The current generated during charge and discharge of the capacitor is (2) (a) Calculate the time derivative of V (t) in Equation (2) using Equation (l) and show that the complex-valued impedance Zc of the capacitor, defined by V(t)= Zc I(t), is Hint: Complex-valued constants are constants for differentiation. (b) Find the current amplitude and show that I(t) is phase-shifted from V(t) by 71/2 (i.e., when V(t) has a maximum or minimum value, O, and vice versa). Hint: write I(t) in exponential form. (c) Find the real parts of V(t) and I(t). Attached file  Thumbnail(s): You must login or register to gain access to this attachment. Read 93 times 2 Replies
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Answer accepted by topic starter
AnonymousAnonymous
wrote...
A month ago

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Anonymous Author
wrote...
A month ago
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