Derive the expression for pulse width in case of a monostable multivibrator?

Question

Derive the expression for pulse width in case of a monostable multivibrator?

Answer 1

In the case of the 555, the voltage across the timing capacitor follows a first order response.

V = Vcc * (1 - exp(-t/RC))

Note that the product RC is simply the time constant

The time starts when the trigger input (pin 2) returns positive.

When this voltage reaches 2/3 of Vcc an internal comparator resets the 555 and the output (pin 3) returns low.

Therefore: 2/3 = (1 - exp(-t/RC))

Solving for t:  t = ln(3) RC or about 1.1 RC

Answer 2

for a 555:

T = 1.1 RC

derive it? nothing to derive. It depends on the internal workings of the 555.