Question

In electrical circuit theory, a circuit C(t) is called a linear circuit. If it satisfies the superposition principle given by C(at1+at2)=aC(t1)+bC(t2), where a,b are constant. Show that the circuit C(t) =3t is linear

Answer 1

Answer:

Concept used:

A function f(x) is said to be linear if

$f(\alpha{x}+\beta{y})=\alpha{f(x)}+\beta{f(y)}$

where

$\alpha\:and\beta$ are constants

Given:

$C(t)=3t$

Now,

$C(a{t_1}+b{t_2})=3(a{t_1}+b{t_2})$

$C(a{t_1}+b{t_2})=3a{t_1}+3b{t_2}$

$C(a{t_1}+b{t_2})=a(3{t_1})+b(3{t_2})$

$C(a{t_1}+b{t_2})=aC(t_1)+bC({t_2})$

Hence C is linear