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DFCCIL Junior Executive Electrical 2018 Official Paper

Option 3 : additivity, homogeneity (symmetry) and time dependent-constants

When a system satisfies the principle of superposition which comprises additivity and homogeneity, then it is said to be linear, else it is a nonlinear system.

__Additivity property__:

If x1(t) → y1(t) and x2(t) → y2(t)

Then x1(t) + x2(t) → y1(t) + y2(t)

__Homogeneity property__:

Ax1(t) + Bx2(t) → Ay1(t) + By2(t

∴ The superposition theorem applies only when all the components of the circuit are linear, which is the case for resistors, capacitors, and inductors. It is not applicable to networks containing nonlinear elements.

__Time invariance:__

- It means that whether we apply an input to the system now or T seconds from now, the output will be identical except for a time delay of T seconds.
- That is, if the output due to input x(t) is y(t), then the output due to input x(t - T) is y(t - T). Hence, the system is time-invariant because the output does not depend on the particular time the input is applied.

**∴ Linear time-invariant systems must satisfy additivity, homogeneity (symmetry), and time dependent-constants**