# Linear Circuit problem with solution video (Network Analysis)

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# Linear network

Linear circuit is a circuit in which all the passive elements parameter like resistance, capacitance, inductance are constant with voltage and current source. and the circuit in which voltage and current sources are independent or directly proportional to the other voltage and current sources or their derivatives is also known as linear circuits.

## Bilateral Network

Bilateral network is the network in which all the passive elements like inductor, resistor, capacitor gives response in both direction of sources. or in other word we can say properties and characteristics of elements are independent of direction of current flow.

## Theory related to above given question

Linear circuit always follows superposition principle that means if we apply linear combination of signal Ax1(t) + Bx2(t) then output F(t) of the circuit will be equal to the linear combination of the outputs due to the signals x1(t) and x2(t) applied separately.

F(Ax1(t) +Bx2(t)) = A.F(x1(t) ) + B.F(x2(t))

# Superposition theorem

Superposition theorem state that the response (voltage or current) in any branch of a linear bilateral network contain multiple sources is equal to the algebraic sum of the response obtain by each source acting separately, during which time all other sources are made zero.

Note – voltage sources is made zero by short circuit and current source is made zero by open circuit.

Note – superposition theorem can not be applied to the power across the elements. Fig-1 Fig-2 Fig-3

### I = I1 + I2

In above figure you can see superposition principle. in fig-1 we have linear circuit and we have to find current I across R2 so to find this current we use superposition principle. in fig to we find current I1 by voltage source by made current source zero then we find current I2 by made voltage source zero. now by superposition principle total current will be

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## December 16, 2019

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