Calculate the impedance in this RC circuit

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SUMMARY

The impedance (Z) in an RC circuit is calculated using the formula Z = sqrt[R^2 + (1/wc)^2]. To find the amplitude and phase of the current, one must express the impedance as a complex number rather than just its modulus. The voltage is given by V = E*cos(wt), and the current can be derived from I = V/Z, where Z includes the imaginary component due to the capacitive reactance (1/jwc). Understanding complex numbers is essential for this analysis.

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  • Complex number manipulation
  • Understanding of RC circuit theory
  • Knowledge of impedance in electrical circuits
  • Familiarity with phasor representation of AC signals
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joelkato1605
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Homework Statement
By calculating impedance, find the amplitude and phase of the current flowing in the
RC circuit shown below (Figure 3.1
Relevant Equations
Z =sqrt[ R^2 + (1/wc )^2]

I=v/Z
1618839771455.png

So Z = sqrt[ R^2 + (1/wc )^2] and V=Ecos(wt) so I= Ecos(wt) / sqrt[ R^2 + (1/jwc )^2] but how do I use this to find the amplitude and phase of the current?
 

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Hi,

Are you familiar with working with complex numbers ?

##\ ##
 
yeah I've done a bit on them
 
Can you write the impedance as a complex number (not only its modulus)?
 
https://www.electrical4u.com/rc-circuit-analysis/#:~:text=An%20RC%20circuit%20is%20defined,RL%20circuit%20or%20RLC%20circuit.
 

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