What is Kirchoff's law: Definition and 67 Discussions

Kirchhoff's circuit laws are two equalities that deal with the current and potential difference (commonly known as voltage) in the lumped element model of electrical circuits. They were first described in 1845 by German physicist Gustav Kirchhoff. This generalized the work of Georg Ohm and preceded the work of James Clerk Maxwell. Widely used in electrical engineering, they are also called Kirchhoff's rules or simply Kirchhoff's laws. These laws can be applied in time and frequency domains and form the basis for network analysis.
Both of Kirchhoff's laws can be understood as corollaries of Maxwell's equations in the low-frequency limit. They are accurate for DC circuits, and for AC circuits at frequencies where the wavelengths of electromagnetic radiation are very large compared to the circuits.

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  1. N

    Solving Kirchoff's Laws: Are My Answers Correct?

    Does anyone know how to do part (a). I labelled the current through R1 I1, I4 through R4, I3 through R3, I2 through R2, and I5 through the 3ohm resistor. I used Kirchoff’s Laws to make the equations I1 + I4 = 8, 2I1 + 32I3 - 14I4 = 30, and I1 + I3 - I4 = 0. I solved these equations by subbing...
  2. Eobardrush

    Help in solving an electricity circuit problem involving Kirchoff's law

    My initial solving method was taking 1.75A and adding the resistors at the 1st loop(4 and 8 ohms) to get the answer V=IR V=1.75(4+8) V=21V But the answer sheet uses 0.75A instead of 1.75A to find EMF of E1. So according to the answer sheet its V=0.75(4+8) V=9V 0.75A is the answer for the i)...
  3. M

    Engineering Kirchoff's Law Problem about this Induction Generator circuit

    Hi, Please find attached below the Induction Generator circuit. I have the following parameters: Parameter Value Rs = Rr (Resistance on stator and rotor) 0.2 Ω Ls = Lr (inductance on stator and rotor) 5 mH = 0.005 H p (number of pairs of poles) 2 f (frequency) 60 Hz Vsl (stator line...
  4. cianfa72

    Relations between ##k## Currents & Voltages for Black-Box Device

    Hi, I'm aware it is an odd question. Consider a ##k##-terminal electrical device as black-box. We know from KLC and KLV that just ##k-1## currents and ##k-1## voltages are actually independent (descriptive currents and voltages). Furthermore we generally expect there exist ##k-1## relations...
  5. Paul Lasdivan

    Engineering Can I solve this using Kirchoff's Law?

    We were given a circuit with 7 resistors and 3 voltage sources For emf sources, ##E_1=120V##, ##E_2=60V##, and ##E_3=30V## while for resistors in ohms,##R_1=10##, ##R_2=5##, ##R_3=20##, ##R_4=8##, ##R_5=12##, ##R_6=6##, ##R_7=8##. Nodes are indicated in small letters (a-j). Loops ##abefa##...
  6. L

    Exploring EMF and Faraday's Law in LR Circuits

    1) Take a non-steady circuit such as an LR circuit. Why does Kirchoff's voltage law work when analyzing such a circuit? Is it because we're assuming that dI/dt and thus dB/dt are approximately zero thus meaning that curl E is approximately zero? 2) ε, the electromotive force, is the line...
  7. fight_club_alum

    Kirchoff's law and circuit analysis

    I assumed the current flows from the 20V so, 20V - 100 (i1) - Ri2 = 0 First loop 20V = 100i1 + Ri2 Second loop +Ri2 + 40V - 200(0.08) = 0 Ri2 = -24 Back to equation 1 20 v = 100i1 + (-24) therefore, i 1 = 0.44 For loop two: i1 - i2 = i3 0.44 - i2 = 0.08 therefore i2 = 0.36 ohms...
  8. J

    Finding the Current in a circuit

    Homework Statement The diagram below shows a circuit where; R1 = 5.0 Ω, R2 = 8.0 Ω, R3 = 1.0 Ω, V1 = 16.8 Volts, V2 = 1.5 Volts, and V3 = 39.6 Volts. What is the value of I1? In solving this problem, initially pick the current directions as shown. If the actual current turns out to be in the...
  9. Felipe Lincoln

    Verifying Kirchoff's law in an AC RLC circuit

    Homework Statement I have the following RLC circuit with an sinusoidal voltage generator and I want to verify the Kirchoff's first law with an oscilloscope. To measure the peak voltage in each of the components I just permute the positions between the component and the resistor. The question...
  10. K

    Black Body vs Non-Black Body: What Sets Them Apart in Kirchoff's Law?

    Homework Statement For a black body all absorbed radiation is emitted. Kirchoff´s law states that at the same temperature T1 the emissivity and absorptivity of a surface are equal, which holds for nonblack bodies as well. So, what really differs a black body and a non-black body in this case?
  11. D

    Kirchhoff's First Law to solve a circuit with 2 loops

    Homework Statement I've recently watched a video which explains Kirchhoff's first law however, I'm not sure about his calculations. I got the same answer just wanting to make sure I am doing it right. the guy wrote L1: -75I2 +3V=0 ⇒ I2= -3/-75=0.04A He calculated L2 like -12V -125I3 +75I2=0 ⇒...
  12. G

    Engineering Simulation of Circuits Without Kirchhoff's Laws?

    1. The problem statement, all variables, and given/known data I am currently drafting a proposal for a project in Computational Physics. I'm planning on creating a program that simulates circuits numerically instead of solving the system of equations. The purpose of my project is to observe the...
  13. E

    Possible confusion regarding application of Kirchoff's Laws?

    Homework Statement Determine Currents ##I_{1}, I_{2}, I_{3}## Homework Equations Kirchoff's Rules: $$\sum_{i=1}^n I_{i} = 0$$ $$\sum_{i=1}^n V_{i} = 0$$The Attempt at a Solution Basically, I'm not sure if I'm applying the Loop Law correctly. For example, in Loop A, going clockwise from...
  14. B

    How Do You Solve Complex Kirchhoff's Law Problems?

    Homework Statement http://file:///Users/jarrettwingfield1/Desktop/Screen%20Shot%202016-09-29%20at%205.29.21%20PM.png My professor told me my equations were correct, but I do not know how to find the current through each resistor mathematically, and every example I find online is too simple...
  15. A

    Current flow model through a resistance field

    Hey everyone. I thought about this problem the other day, but I don't know what theory I need to solve this problem. Given a 2D rectangle with a known, varying resistance, and a known voltage drop across the length, how would one calculate the current density at each point on the surface. By...
  16. O

    Kirchoff's Law -- Having issues with the some signs

    Homework Statement Having issues with the some signs when applying kirchhoffs law. When you take the derivative of charge with respect to time, is it always -i? I figured if it's charging, the change in charge with respect to time would be the same as just i, but if it's discharging then it...
  17. R

    Find the Resistor Size for 160W Power Delivery: Kirchoff's Law Question"

    Homework Statement In the circuit shown, what must be the size of the resistor R such that the power delivered to the 8 Ω resistoris 160 Watts? Circuit is in the first image Homework Equations ∑I at Junction= 0 ∑ΔV though loop=0 P=I2R ΔV=ε-Ir The Attempt at a Solution The circuit I have...
  18. Toon

    Kirchoff's law help with circuits

    Homework Statement The circuit to the right consists of a battery (V0 = 26.0 V) and five resistors (R1 = 211 Ω, R2 = 682 Ω, R3 = 363 Ω, R4 = 534 Ω, and R5 = 465 Ω). Find the current passing through each of the specified points. The Circuit http://i.imgur.com/4JSIHdG.png all I need to find is Ih...
  19. C

    Understanding Kirchoff's Law: Solving for Current and Voltage in a Circuit

    Homework Statement See the picture. I have to find ## i ## and ## u_{ab} ##. Homework Equations [/B]Well, as the thread name says, Kirchoff law ## \sum_{k=1}^{n} i_k=0 ## , that is algebraic sum of currents in one point is 0. The Attempt at a Solution Well, first I tried to set up few...
  20. J

    MHB Kirchoff's Law equation 3 unknowns Help

    Please could somebody help me with this Kirchoff's law question with explanations/working out? I've been on it for hours and cannot see where I'm going wrong! Q. An electrical circuit comprises three closed loops giving the following equations for the currents i1, i2 and i3. i1 + 8i2 + 3i3 =...
  21. F

    Kirchoff's Law - Wire in parallel with light bulb

    Homework Statement If you measure the resistance of the three lightbulbs (independently) and get the following values. What is the equivalent total resistance of the circuit, and it’s uncertainty. R_1 = (50 \pm 7) \Omega, \ \ R_2 = (720 \pm 30) \Omega, \ \ R_3 = 140 \pm 20) \Omega Now you...
  22. Sunny Singh

    Apparent violation of kirchoff's law of thermal radiation

    suppose there are two bodies A and B with emissive powers e1 and e2 respectively and with absorptive powers a1 and a2 respectively... now both bodies are at the same temperature T. Hence e1/a1 = e2/a2 = const by kirchhoffs law. for the body A, energy emitted is e1 and...
  23. O

    Confused about Kirchoff's Law: How is the current calculated in this problem?

    Homework Statement Homework Equations There is not really a relevant attempt at a solution. I do however have the following question: According to the solutions and some reverse 'engineering' I found out that the voltage across R2 is the same as U1 = 60V. It's been years since I've done...
  24. R

    Kirchoff's Law: Solving a Circuit with Parallel Components

    Homework Statement Homework Equations V= iR Kirchoff's law for voltage The Attempt at a Solution On the left-most part of the circuit , I did use KVL (voltage law) and I ended up with Vs = i0 (R1+R2) which basically boils down to i0(2R) since R1 = R2 =R3 ... I'm not even...
  25. E

    Engineering A Kirchoff's Law problem with a bridge circuit

    Homework Statement I want to use Kirchoff's current law to analyze the pictured curcuit and find the current drawn fro the voltage source between the positive terminal and node 1. [PLAIN]http://s42.photobucket.com/user/Jemspak/media/circuitdiagram.jpg.html" (i can't figure out how to...
  26. P

    How Does Kirchoff’s Voltage Law Apply to Supernodes in Circuit Analysis?

    Hello All, I am trying to teach myself basic EE. The textbook I am using gave the following example: 1. Find IS2. Diagram is attached. Given: IS1 = 2A I2 = 3A I3 = 2A I4 = 1A I5 = 0A The answer in the textbook is 1A. My Method using KCF: IS1 + IS2 - I2- I3 - I4 -I5 = 0...
  27. R

    Why is the current not zero in part e of this Kirchoff's Law problem?

    http://i.imgur.com/EFciS60.png How do you do part e? Also can someone explain why the current I3 isn't 0 if the switch has been closed for a long time? Doesn't it behave like a short circuit if the switch is closed because the capacitor becomes fully charged and the current becomes zero ish?
  28. D

    How do I find the current through each resistor using Kirchoff's laws?

    Homework Statement See attached image. Suppose I want to find the current through each resistor…how would I do so? Homework Equations Kirchoffs eqns … sum of voltages around every loop is zero The Attempt at a Solution 1. The first problem I have with this, is that i am...
  29. O

    Finding the Number of Currents in a Circuit: Tips and Intuition

    For the following circuit: How would you deduce the number of currents there are? I am having trouble predicting how many are there (i am convinced there are 3). Also, in general, what are some tips for finding how many currents there are?
  30. Y

    How to Apply Kirchoff's Laws to Solve Resistive Circuit Problems

    Homework Statement In the following figure(Figure 1) the battery has emf 26.0V and negligible internal resistance. R1 = 4.10Ω . The current through R1 is 1.50A and the current through R3 = 5.00A What are the resistances of R2 and R3? (Image Attached) Homework Equations Kirchoff's...
  31. Z

    Circuits involving Kirchoff's law

    Homework Statement Determine the currents I_1,I_2,I_3 given the information below. Note that the directions of the currents are drawn by myself. All other info was given at start. http://i.imgur.com/Pw2KK3O.jpg Homework Equations Kirchoffs law The Attempt at a Solution...
  32. S

    Complex circuits with Kirchoff's law

    I have the diagram on the right, I've set up a few equations to solve... My calculator tell me mathematical error. can someone point out the error? thanks. http://img21.imageshack.us/img21/5395/imgyqc.jpg
  33. M

    Find Current Through Voltage Source Using Kirchoff's Law

    Homework Statement I need to find the current through the 3V voltage source: picture of the circuit and the equations there: vantraveller.blogspot.ca The Attempt at a Solution I was about to get 3 equations, however, I find myself having 5 unknowns, what other equations can I write...
  34. W

    Kirchhoff's Law Help: Solve Voltage & Current for Circuit

    Homework Statement http://imgur.com/DuBgK Homework Equations I1=I2+I3 Sum of the directed potential differences around any closed loop equals zero The Attempt at a Solution I worked out the total resistance which came out to be 4.5Ω [3 + 1/(1/6+1/2)] But now I don't know which...
  35. C

    A kirchoff's law question with multiple batteries

    Homework Statement To find the voltage at the 5 ohms resistor. Homework Equations V=IR Kirchoff's first and second law The Attempt at a Solution The attempt was simply too long I ended up with a voltage of 6.5V on the 5 ohm resistor... Please help me, I have been stuck in this...
  36. G

    Solving Kirchoff's Law Questions: Finding Current Direction

    kirchoff's law?? Hi Sometimes in kirchhoffs law questions it gives the circuit without showing the direction of the current so how do I determine the direction of the current (not the direction that I choose to solve the question)? please help! I have exam tomorrow
  37. A

    A doubt regarding the proof of kirchoff's law of thermal radiation

    In the proof that I have studied, there is a Isothermal cavity that behaves as a black body. there is another small opaque body inside the cavity at the same temperature with emissivity e, absorptivity a and area s. now the irradiation on the small body is Eb = σ times T raised to 4. now the...
  38. J

    Why Does the Sign of dq/dt Change in RC Circuit Equations?

    I can't figure out the differential equation made in RC circuits During charging E = iR + q/C ...I understand this During discharging my book says that since E = 0 , iR + q/C = 0 and by using i = dq/dt it solves the equation But using kirchhoffs law i end up with the equation q/C - iR = 0...
  39. X

    Finding the Potential (Kirchoff's Law)

    Homework Statement http://puu.sh/i8Bg Homework Equations V=IR ƩV = 0 The Attempt at a Solution Starting behind the left EMF source I sum the potential changes using Kirchoff's Voltage Law 150V - R2I - 50V - R1I = 0 Solving for I, I get 20Amps However I know this can't be right...
  40. U

    Circuits, Kirchoff's Law for Nodes

    Homework Statement Hello, This is part of a set of questions I need to do for a project I just need help getting started. I've been looking at this forever and I can't figure it out. Homework Equations Kirchhoff's Law for Nodes: Current going into a node = current going out...
  41. teroenza

    Kirchoff's Law With Battery Only

    Hello, If one had a resistance free wire and a battery with no internal resistance, how would Kirchoff's law be applied if the terminals of the battery were connected by the wire? Is this even an appropriate question? I know/believe current would be at infinity. I am still trying to fully...
  42. M

    Applying Kirchoff's law to circuit which only has cells

    Homework Statement Find the Voltage across A B in the following circuit. Each cells has negligible internal resistance and an EMF of E volts. (First diagram in the attached picture) Homework Equations I'm trying to use Kirchoff's second law. The Attempt at a Solution Now, if I...
  43. E

    Kirchoff's Law Question; I'm very close

    Homework Statement Two batteries and three resistors are connected as shown in the figure. How much current flows through the 6.0V battery when the switch is closed? How much current flows through the 9.0V battery when the switch is closed? How much current flows through the 6.0V battery...
  44. P

    Engineering Circuit Element Question using Kirchoff's law

    Homework Statement http://img137.imageshack.us/img137/355/circuit2.png Homework Equations P=VI P=I^2 R V=IR The Attempt at a Solution The part a is all correct. i_\wedge = 5A i_o = 2A v_o = 80V This is what i have done in part b but it is not correct because P_delivered not equal to...
  45. W

    RL Circuit: Kirchoff's Law is Wrong - Faraday's Law is Correct

    Hi Guys, This is going to be a bit controversial but that's ok. In an RL circuit, both with and without a battery, Kirchoff's law is invoked in virtually every elementary textbook in the United States and perhaps in the world. It is a mistake! The voltage drop across an inductor is...
  46. T

    Kirchoff's Law: Identifying Loops in Circuits

    Homework Statement I am doing Kirchoff's law and i have problems in identifying different loops in a circuit, especially multiple loops. For example, in my attachment for diagram 1, there are 2 loops(ABCFA and ABCDEFA) ? But for diagram 2, the loops are ABCFA and CDEFC?
  47. A

    Calculate voltage drop by using kirchoff's law

    Homework Statement The circuit has a battery Voltage of 30V, a resistor of R1(8ohms), R2 (2Ohms) and R3 (4ohms) in series. Calculate the voltage drop over R1 Homework Equations Please give me the proper equation of this? The one I've got says you take 30-8I-2I-4I=0 Wich gives you...
  48. S

    Applying Kirchoff's Law to a Short-Circuited Resistor: Where Is the Fallacy?

    In the attachment (also given at bottom for your convenience) you can see the circuit diagram. We all know that the 5 ohm resistor is short-circuited so no current flows through the resistor. But if we apply Kirchoff's loop law with the following symbols: i = current through DBAC from positive...
  49. R

    Approximate the voltage with Kirchoff's law

    Homework Statement Kirchoff's first law gives the relationship E(t) = L * (di/dt) + R*i where L is the inductance, R is the resistance and i is the current. \begin{tabular}{|c|c|c|c|c|c|} \hline $\emph{t}$ & 1.00 & 1.01 & 1.02 & 1.03 & 1.04\\ \hline $\emph{i}$ & 3.10 & 3.12 & 3.14 &...
  50. C

    The Comfort Inside Igloos & Snowcaves Explained by Kirchoff's Law

    Snow behaves like a black-body with respect to infrared radiation. Given this fact, explain why is it not surprising that inhabited igloos and snowcaves are characterized by comfortable temperatures inside. HINT: (Kirchoff's Law will help explain this)