A 12 V battery has been connected to an L R circuit for sufficient time so that

Question

A 12 V battery has been connected to an LR circuit for sufficient time so that a steady current flows through the resistor R=2.2k and inductor L=18mH. At t=0, the battery is removed from the circuit and the current decays exponentially through R.

A.)

Write the equation for the emf across the inductor as a function of time t.

Express your answer in terms of the variables V (the voltage of the battery), R, L, t, and appropriate constants.

B.)

At what time is the emf greatest?

C.)

What is this maximum value (V)?

Explanation / Answer

Emf of the battery Eo = 12 volt

resistance R=2.2k= 2200 ohm

inductance L=18mH= 0.018 H

In RL circuit ,current at time t is i = io e -(R/L)t

                                           i R= ioR e -(R/L)t

                                            E = Eo e -(R/L)t

When time t= 0 , E = Eo e 0

                             = Eo

i.e., at time t= o emf is maximum.

Maximum value of V is =Eo = 12 volt

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