Kirchhoff's laws for an electric circuits

Kirchhoff's laws: Kirchhoff had given two laws for electric circuits i.e.
  1. Kirchhoff's Current Law or Junction Law

  2. Kirchhoff's Voltage Law or Loop Law
  1. Kirchhoff's Current Law or Junction Law: Kirchhoff's current law state that

    The algebraic sum of all the currents at the junction in any electric circuit is always zero.

    $\sum_{1}^{n}{i_{n}}=0$

    Sign Connection: While applying the KCL, the current moving toward the junction is taken as positive while the current moving away from the junction is taken as negative.
    Flow of Current in a Junction
    The flow of Current in a junction
    So from figure,the current $i_{1}$,$i_{2}$,$i_{5}$ is going toward the junction and the current $i_{3}$,$i_{4}$, So

    $\sum{i}= i_{1}+i_{2}+(-i_{3})+(-i_{4})+i_{5}$

    According to KCL $\sum{i}= 0$, Now the above equation can be written as

    $i_{1}+i_{2}+(-i_{3})+(-i_{4})+i_{5}=0 \qquad$

    $i_{1}+i_{2}+i_{5}=i_{3}+i_{4}$

    Thus, the sum of current going towards the junction is equal to the sum of current going away from the junction.

    In other words, at any junction, neither the charge accumulates nor the charge is removed. So this law represents conservation of charge.


  2. Kirchhoff's Voltage Law or Loop Law: Kirchhoff's voltage law state that:

    The algebraic sum of all the voltage or emf in any closed loop of an electric circuit is always zero.

    $\sum_{1}^{n}{E_{n}}=0$

    This means that the algebraic sum of all the emf applied in any closed loop is always equal to the algebraic sum of the product of current and resistance in the closed loop.

    $\sum{E}=\sum {i.R}$

    Sign Connection: While applying this law, a product of current and resistance is taken as positive when we traverse in the direction of the conventional current and the emf is taken positively when we traverse from negative to the positive electrode through the electrolyte.
    Distribution of current in a loop of circuit
    Distribution of Current in a Loop of Circuit
    So from the figure:

    For Mesh $(1)$

    $E_{1}-E_{2}=i_{1}R_{1}-i_{2}R_{2} \qquad(1)$

    For Mesh $(2)$

    $E_{2}=i_{2}R_{2}+\left( i_{1}+i_{2} \right)R_{3} \qquad(2)$

Popular Posts

Study-Material













  • Classical world and Quantum world

  • Inadequacy of classical mechanics

  • Drawbacks of Old Quantum Theory

  • Bohr's Quantization Condition

  • Energy distribution spectrum of black body radiation

  • Energy distribution laws of black body radiation

  • The Compton Effect | Experiment Setup | Theory | Theoretical Expression | Limitation | Recoil Electron

  • Davisson and Germer's Experiment and Verification of the de-Broglie Relation

  • Significance of Compton's Effect

  • Assumptions of Planck’s Radiation Law

  • Derivation of Planck's Radiation Law

  • de-Broglie Concept of Matter wave

  • Definition and derivation of the phase velocity and group velocity of wave

  • Relation between group velocity and phase velocity ($V_{g}=V_{p}-\lambda \frac{dV_{p}}{d\lambda }$)

  • Group velocity is equal to particle velocity($V_{g}=v$)

  • Product of phase velocity and group velocity is equal to square of speed of light ($V_{p}.V_{g}=c^{2}$)

  • Heisenberg uncertainty principle

  • Generation of wave function for a free particle

  • Physical interpretation of the wave function

  • Derivation of time dependent Schrodinger wave equation

  • Derivation of time independent Schrodinger wave equation

  • Eigen Function, Eigen Values and Eigen Vectors

  • Postulate of wave mechanics or Quantum Mechanics

  • Quantum Mechanical Operators

  • Normalized and Orthogonal wave function

  • Particle in one dimensional box (Infinite Potential Well)

  • Minimum Energy Or Zero Point Energy of a Particle in an one dimensional potential box or Infinite Well

  • Normalization of the wave function of a particle in one dimension box or infinite potential well

  • Orthogonality of the wave functions of a particle in one dimension box or infinite potential well

  • Eigen value of the momentum of a particle in one dimension box or infinite potential well

  • Schrodinger's equation for the complex conjugate waves function

  • Probability Current Density for a free particle in Quantum Mechanics

  • Ehrenfest's Theorem and Derivation

  • Momentum wave function for a free particle

  • Wave function of a particle in free state

  • One dimensional Step Potential Barrier for a Particle

























  • Blog Archive