the frequency of the input triggered signal is 1 KHz with 75% duty cycle. If the value of C is 0.01 micro-Farads, what is the value of external resistance (in K Ohms)?

To calculate the value of the external resistance (R) in a circuit with a given frequency (f) and duty cycle, we can use the formula for the frequency of a 555 timer in astable mode:

f = 1.44 / ((R1 + 2*R2) * C)

Where:

• f is the frequency,
• R1 and R2 are resistances, and
• C is the capacitance.

Given that the frequency (f) is 1 KHz and the capacitance (C) is 0.01 micro-Farads, we can rearrange the formula to solve for the total resistance (R1 + 2*R2):

R1 + 2*R2 = 1.44 / (f * C)

Substituting the given values:

R1 + 2R2 = 1.44 / (1 KHz * 0.01 micro-Farads) R1 + 2R2 = 144 K Ohms

In a 555 timer circuit with a 75% duty cycle, the resistances R1 and R2 relate to the duty cycle as follows:

Duty cycle = R2 / (R1 + 2*R2)

Rearranging to solve for R2:

R2 = Duty cycle * (R1 + 2*R2) R2 = 0.75 * 144 K Ohms R2 = 108 K Ohms

Substituting R2 back into the equation for the total resistance:

R1 + 2*108 K Ohms = 144 K Ohms R1 = 144 K Ohms - 216 K Ohms R1 = -72 K Ohms

However, resistance cannot be negative. This suggests that there may be an error in the problem as stated. Please check the given values and try again.