Question

2. [25] Home security systems use inductive sensors to monitor doors and windows. Suppose model one of these sensors as a resistor and inductor in series, as shown below, and that closing the door or window is equivalent to closing the switch as shown. This is equivalent to applying a step input with an amplitude of 5 V. If L 20 mH and R 20 , find the we can (a) Differential equation in terms of vo(t). Note: leave v:(t) as a generic input (variable) until part (d) (b) Transfer function from vi(t) to vo(t) (c) Pole/zero diagram (d) Time-domain response to v:(t) =5u,(t) V (e) Final value of the response t 0 IL L + + R vo(t) 5 V (1)°a (1)la

Answer 1

t-o No (t) 5V a). -Ld dt iR-O V: (-t) Vilt) -Vo (t) 0. -L d Cb). Vo(s) 5V L (R+ SL) 51 Vo()= R+SL CC Pole fo t Ree) L

(d) 5L Vols) R+SL CDe knowthat ulA) ots) 20 20 10 Vol-t) 5 e Se lcot 5 e lcoot 5 Ce), FVt Resporge 1000t 52 Volt)- at t-o Volt) - o