Concepts Of Physics MCQ Edition [Volume 2]PhysicsElectromagnetic Induction
An LR circuit features L = 1.0 H and R = 20 . At t = 0 , it is connected across a 2.0 V emf. Calculate the rate of change of current di/dt at t = 1.0 s .
Options
- A2.0 10⁻⁹ A s ⁻¹
- B8.2 10⁻⁹ A s ⁻¹
- C4.1 10⁻⁹ A s ⁻¹
- D4.1 10⁻⁸ A s ⁻¹
Correct answer
C. 4.1 10⁻⁹ A s ⁻¹
Step-by-step solution
The current in an LR circuit during growth is given by: i = E R (1 - e^ -Rt/L ) Differentiating with respect to time t , we get the rate of change of current: di dt = E L e^ -Rt/L Substituting the given values E = 2.0 V , L = 1.0 H , R = 20 , and t = 1.0 s : di dt = 2.0 1.0 e^ -20 1.0 / 1.0 di dt = 2.0 e⁻²⁰ Using the value e⁻²⁰ 2.06 10⁻⁹ : di dt 2.0 2.06 10⁻⁹ = 4.12 10⁻⁹ A s ⁻¹