In an inductor, the current changes from 0 A to 10 A uniformly in 20 sec time. The induced voltage is 2 V. What is the inductance of the inductor?

Concept:

The voltage induced in the inductor is given as

\({V_L} = L\frac{{di}}{{dt}} = L\frac{{\left( {{i_2} - {i_1}} \right)}}{{\left( {{t_2} - {t_1}} \right)}}\)

Where,

L = Inductance

i₂ = Final value of current

i₁ = Initial value of current

t₂ = Final time

t₁ = Initial time

Calculation:

Given-

i₁ = 0 A, i₂ = 10 A, V_L = 2 V

t₁ = 0 sec, t₂ = 20 sec

\(\therefore 2 = L\frac{{\left( {10 - 0} \right)}}{{\left( {20 - 0} \right)}}\)

\(L = \frac{{2 \times 20}}{{10}}\)

L = 4 H