Question

1.Two coils are connected inseries with inductance L1 and L2.Find the expression for their effective inductance.

Answer 1

Let the voltage drops across the teo inductors be V1 and V2 respectively. Now, we know that the equivalent voltage drop across the entire system will be

V = V₁ + V₂ .............................(1)

also, these voltages can be expressed as

V = L.(dI/dt)

V₁ = L₁.(dI₁/dt)

and

V₂ = L₂.(dI₂/dt)

now as the two inductors are in series the current in both of the will be teh same.

so,

I₁ = I₂ = I

so, equation (1) becomes

L.(dI/dt) = L₁.(dI₁/dt) + L₂.(dI₂/dt)

thus, we get

L = L₁ + L₂

the individual inductances get added.