A 12 V car ignition coil has an inductance of 10 mH and resistance of 2 Ω (so its equivalent circuit is a 10 mH inductor in series with a 2 Ω resistor). Calculate how long it takes the current to build up to 95% of its maximum value after a 12 V battery is connected to the coil?

t = 0.01497 s

Explanation:

This series RL circuit is described by the expression

        I = I₀ (1 - )

where τ = L / R

Let's clear

         I / I₀ = 1 - e^{-t/\tau }

         e^{-t/\tau  } = 1 - I / I₀

          t /τ = ln (1- I/I₀)

In our case

          I / I₀ = 0.95

         -t /τ = ln (1 -0.95)

         -t /τ = -2.9957

          t = 2.9957 τ = 2.9957 (10 10⁻³ / 2)

          t = 0.01497 s

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