In electrical circuit theory, a circuit C(t) is called a linear circui

1.	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) = 31 is linear.
Answer» Given C(t) = 3t. To prove that the function is linear C(at₁) = 3a(t₁) C(bt₂) = 3 b(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.

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) = 31 is linear.

Answer»

Given C(t) = 3t.

To prove that the function is linear

C(at₁) = 3a(t₁)

C(bt₂) = 3 b(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.