#### Equivalence:

In series circuit equivalent circuit is formed by simply adding resistance values. In parallel circuits first we take the reciprocal of resistances and add them. it’s equivalent is = V1 – V2 it’s equivalent is = I1 – I2

#### Linearity:

All the circuits which we discussed earlier are linear circuits because they contain only one element. Linear circuits can be series or parallel circuits. #### Superposition:

As we are moving circuits are becoming more complex for this we prefer to use superposition theorem. This theorem provides us the ability to reduce a complex circuit into different small parts so we can easily  solve them while each of them contain a single independent source.

In any linear circuit containing multiple independent sources, the current or voltage at any
point in the network may be calculated as the algebraic sum of the individual contributions of each source acting alone.

Example: Find V0 by using superposition There are 2 sources in this circuit first we remove voltage source then the circuit take form so first we calculate I0 by current division

I0=(2mA) (1k + 2k) / (1k + 2k + 6k)

I0 = 2 / 3 mA

equation for v’o is

v’o=I0.R

v’o = (2 / 3) m. 6k                 =4V

now remove current source and the circuit will take form now calculate v”o by voltage division

v”o = (6k) / (6k)(3k) . 3

=2V

we know that                                                                    V0 = V’o + V”o

V0 = 2+4

V0 = 6V

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