A coil with a resistance of 40 is connected across a 4.0 V battery. If the current in the coil is 63 mA exactly 0.10 s after making the connection, determine the inductance of the coil.

Step-by-step solution

The growth of current in an LR circuit is given by the equation: I = I₀(1 - e^ -Rt/L ) The steady state maximum current I₀ is: I₀ = V R = 4.0 40 = 0.1 A = 100 mA Given that the current I = 63 mA at time t = 0.10 s , substituting these values into the equation gives: 63 = 100(1 - e^ -40 0.10 / L ) 0.63 = 1 - e^ -4.0/L e^ -4.0/L = 1 - 0.63 = 0.37 Since e⁻¹ 0.37 , equating the exponents gives: 4.0 L = 1 L = 4.0 H