MHB Current Equivalence at a Circuit Node

AI Thread Summary
The discussion focuses on applying Kirchhoff's Current Law (KCL) to a specific circuit node. It explains that the incoming current through resistor R1 must equal the sum of the outgoing currents through the capacitor, a non-linear resistor, and an inductor. The equation presented, \(\frac{e - v_c}{R_1} = C\frac{dv_c}{dt} + f(v_c) + i_L\), represents this balance of currents. Participants seek clarification on the specific currents and node referenced in the explanation. Understanding these relationships is crucial for analyzing circuit behavior accurately.
Dustinsfl
Messages
2,217
Reaction score
5
Given the circuit below:

4BotojH.png


Why does KCL equate to
\[
\frac{e - v_c}{R_1} = C\frac{dv_c}{dt} + f(v_c) + i_L
\]
 
Mathematics news on Phys.org
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?
 
Thread 'Video on imaginary numbers and some queries'
Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Thread 'Unit Circle Double Angle Derivations'
Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...

Similar threads

Replies
3
Views
2K
Replies
4
Views
1K
Replies
2
Views
2K
Replies
14
Views
199
Replies
10
Views
407
Replies
7
Views
1K
Back
Top