$1.$ Consider the monostable multivibrator using the $555$ timer.$$ R is $15$kohm, and C is $20$uF$.$ Vcc is $12$V$.$

a$.(10$ points$)$ What is the minimum trigger voltage that produces an output pulse?

b$.(6$ points$)$ What is the maximum capacitor voltage or threshold voltage?

c$.(6$ points$)$ What is the pulse width?

d$.(6$ points$)$ If it is desired to have a pulse generated for every trigger, what is the minimum trigger frequency?

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