A 12 V battery has been connected to an LR circuit for suffi

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)?

Solution

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