Question

In electrical circuit theory, a circuit C(t) is called a linear circuit if it satisfies the superposition principle given by C(at₁ + bt₂) = aC(t₁) + bC(t₂), where a, b are constants. Show that the circuit C(t) = 3t is linear.

Answer 1

Given C(t) = 3t

To prove that the function is linear

C(at₁) = 3a(t₁)

C(bt₂) = 3b(t₂)

C(at₁ + bt₂) = 3[at₁ + bt₂] = 3at₁ + 3bt₂

= a(3t₁) + b(3t₂) = a[C(t₁) + b(Ct₂)]

∴ Superposition principle is satisfied.

Hence C(t) = 3t is linear function.