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    Mesh current method

    The Mesh Current Method is used to calculate electric circuits with more than one loop. Calculating mesh means to find the currents in all mesh branches. Both Kirchhoff's laws are the basis for that method.

    The First Kirchhoff's law says that the total algebraic sum of all branch currents, which are connected to the node, is zero. Some currents are flowing to the node, some are leaving the node, but the total is zero, because the node is not able to accumulate electric charge.

    first kirghofs law
    I1−I2−I3=0I_{1} - I_{2} - I_{3} = 0

    The Second Kirchhoff's law says that the total sum of voltages on resistive elements within a loop is equal to the sum of all voltage sources within that loop.

    ∑kRk⋅Ik=∑nEn\sum_{k} R_{k}\cdot I_{k} = \sum_{n} E_{n}

    Consider the following mesh, which we need to calculate: