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Lets have a look at another parallel circuit.

We see therefore that 1 / total resistance = the sum of the inverse resistances of the individual resistors.
The total current through the battery in the above circuit is also the sum of the currents through the resistors.

Now lets have a look at the current law of Kirchhoff.

We see four currents going into a node. Some of these currents may be negative and thus actually be going out of the node.
There is very little space on this node for any charge accumulation. The charge on the node is so small it may be ignored.
The rate of change of the charge going into the node is given by dQ/dt = total current into the node
So dQ/dt = I₁ + I₂ + I₃ + I₄
But dQ/dt = 0 , so I₁ + I₂ + I₃ + I₄ = 0
The total current going into a node is therefore zero. This is KCL or Kirchhoff's current law.

Go to an example on reducing a circuit

Go to an example on using KVL and KCL

Go to an example on using Thevenin equivalents


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