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- Homework Statement
- An inductor, two resistors, a make-before-break switch, and a battery are connected as shown. The switch throw has been at contact e for a long time and the current in the inductor is 2.5A. Then, at t=0, the switch is quickly moved to contact f. During the next 45ms the current in the inductor drops to 1.5A. If the resistors are both have value 0.4Ω, what is the value of the inductance L in H?

- Relevant Equations
- Kirchhoff's loop rule

$$I(t) = \frac{\varepsilon}{R}(1 - e^{\frac{-Rt}{L}})$$

When the current has been running for a while we can treat the circuit connected to e like a battery with two resistors. The current at this point is 2.5 A so using kirchhoff's loop rule we find that the emf of the battery is 2V. $$\varepsilon - IR - IR = 0$$

When the switch flips to f, we can use the current function to find L since we know the current (1.5 A) at a particular time. $$I(t) = \frac{\varepsilon}{R}(1 - e^{\frac{-Rt}{L}})$$

Plug in 1.5 for I, 2 for ##\varepsilon##, 0.4 for R, 45 ms for t and solve for L. Where did I go wrong? Thank you