Current Equivalence at a Circuit Node

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SUMMARY

The discussion centers on Kirchhoff's Current Law (KCL) as applied to a specific circuit involving a resistor (R1), a capacitor (C), a non-linear resistor (f(vc)), and an inductor (iL). The equation derived from KCL is \(\frac{e - v_c}{R_1} = C\frac{dv_c}{dt} + f(v_c) + i_L\), indicating that the current entering the node through R1 equals the sum of the currents leaving the node through the capacitor, the non-linear resistor, and the inductor. The participants emphasize the importance of understanding the flow of current at the node to grasp the application of KCL in this context.

PREREQUISITES
  • Understanding of Kirchhoff's Current Law (KCL)
  • Familiarity with circuit components: resistors, capacitors, and inductors
  • Basic knowledge of differential equations in circuit analysis
  • Experience with non-linear functions in electrical engineering
NEXT STEPS
  • Study the application of Kirchhoff's Current Law in complex circuits
  • Learn about the behavior of non-linear resistors in circuit analysis
  • Explore differential equations related to capacitor charging and discharging
  • Investigate the role of inductors in transient circuit response
USEFUL FOR

Electrical engineers, circuit designers, and students studying circuit analysis who need to deepen their understanding of KCL and its application in analyzing complex circuits.

Dustinsfl
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Given the circuit below:

4BotojH.png


Why does KCL equate to
\[
\frac{e - v_c}{R_1} = C\frac{dv_c}{dt} + f(v_c) + i_L
\]
 
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dwsmith said:
Given the circuit below:

4BotojH.png


Why does KCL equate to
\[
\frac{e - v_c}{R_1} = C\frac{dv_c}{dt} + f(v_c) + i_L
\]

KCL says that in any node current in equals current out.

In the node at the top, the current through $R_1$ is coming in, which must therefore be equal to the current going out and into the capacitor plus the current through the non-linear resistor plus the current through the coil.
 
I like Serena said:
KCL says that in any node current in equals current out.

In the node at the top, the current through $R_1$ is coming in, which must therefore be equal to the current going out and into the capacitor plus the current through the non-linear resistor plus the current through the coil.

I still don't quite understand. Can you be more specific by node at the top and the currents you mention?
 

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