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The frequency of a 555 Timer IC in astable mode is given by:

[f = \frac{1.44}{{(R1 + 2R2) * C1}}]

Here

Please replace the (R1), (R2), and (C1) with the actual values from your circuit to calculate the frequency of oscillation.

At 555 pins 2,6 and 7 are connected. What is the frequency formula?

I have only 1 resistor

In a 555 Timer running in astable mode with just one resistor (R1) and one capacitor (C1), the circuit becomes a simple oscillator and the frequency of operation is determined by the discharge of capacitor through resistor R1.

In this simplified configuration, the charge time ((t_{charge})) is approximately 0.693 times R1*C1 and the discharge time ((t_{discharge})) is very small and can be ignored.

[t_{charge} \approx 0.693 * R1 * C1] [t_{total} = t_{charge} + t_{discharge} \approx t_{charge}]

The frequency of oscillation in this case is then given by the inverse of the total time period:

[f = \frac{1}{t_{total}} \approx \frac{1}{t_{charge}}]

So, the frequency is approximately:

[f \approx \frac{1}{0.693 * R1 * C1}]

Please substitute the actual values of your R1 and C1 in this formula to get the frequency. Remember that this is a simplified circuit and the real behavior might be slightly different due to the discharge time not being totally negligible and other elements in real world components and circuits.

Frequency of the signal is 20kHz, R = 5k1, C = 10nF. What is the formula?

In order to set up a 555 timer in astable mode with a specific frequency, we ordinarily require two resistors. However, given there is only one resistor present in this case, we must assume that the charge and discharge times of the capacitor are the same.

The time period (T) of one complete cycle of a wave is given by:

[T = 0.693 * R * C]

Where:

The frequency (f) is the inverse of the time period:

[f = \frac{1}{T} = \frac{1}{0.693 * R * C}]

Given the resistor R = 5.1kΩ (or 5100 Ω) and the capacitor C = 10nF (or 10 x 10^-9 F), the frequency you're aiming for is 20kHz (or 20 x 10^3 Hz), we can arrange the formula for the required resistance as;

[R = \frac{1}{0.693 * f * C}]

By substituting the given values into the above equation, we should be able to calculate the exact value for the resistor needed to generate a 20kHz signal. Please note that the simplified circuit and frequency calculation might not precisely match the real behavior due to the non-negligible discharge time and other real-world factors.