Solving Equivalent resistance of complex circuits

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Here equivalence solved for resistance, it can also be applied to capacitance and impedance. Solving method for electric circuit problems such as to find equivalent resistance between points a and b in a circuit is explained here.

Here I introduce circuit text form, it is a way of denoting circuit in written form. First we should know about it.

Circuit Text Form

Circuit text form is a notation for representing series and parallel connection between circuit elements. Symbols are used for series and parallel combination, number values are represent resistor element resistance.

After writing the circuit text form try using our equivalent resistance calculator to solve circuit automatically and avoid multiple calculations, get result instantly.

How to differentiate between resistor series or parallel arrangement:

Number of Current flowing paths between two nodes is factor in finding type of block.

If there is one path between two nodes then it is series arrangement. Else if there are multiple paths then it is parallel arrangement.

How to find Equivalent Resistance

equivalent resistance of complex circuit

There are four steps to solve a complex circuit

  1. Redraw the circuit into a simple form.
  2. Label all the nodes in the circuit.
  3. Divide the circuit into blocks which are series or parallel.
  4. Solve equivalence blocks.

Remove paths that has no electrical elements and merge end nodes of the path. Here path means path between two nodes. Keep any one of the node label. When two nodes are merged, one or more extra path is added to node.

Redrawing is done such that series and parallel paths easily identifiable.

Identify zero level series and parallel blocks. Zero level blocks contain resistors alone. Higher level blocks formed with zero level blocks, higher level blocks and resistors.

Solve first the zero level blocks. Then gradually solve higher level blocks.