I am a student trying to build a circuit of traffic light using 555circuit.
I am confused how to calculate the time constant of this circuit.
Can I get a help how to find the time constant for this circuit?

 

Welcome to AAC!

Since you're a student, you'll learn/retain more if you put in the effort to understand the circuit.

When power is first applied, the outputs of both timers will be HIGH. Do you know how calculate the time required for the timing capacitors to charge to 8V (or can you read the datasheet to find out)?

 

Welcome to AAC!

Since you're a student, you'll learn/retain more if you put in the effort to understand the circuit.

When power is first applied, the outputs of both timers will be HIGH. Do you know how calculate the time required for the timing capacitors to charge to 8V (or can you read the datasheet to find out)?

Thank you so much!
I'll try my best

 

Perhaps this will help:
555 Timer Functional Operation Explained--
The 555 timer is one of the most widely used analog ICs ever made, but its principles of operation are not always clear from the data sheet, so here's a short, and hopefully clearer, explanation of that.

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The 555 operation is fairly simple.
It is basically a level-triggered flip-flop (latch) with an added DIScharge output to reset the timing capacitor.
The trigger levels are determined by the three 5kΩ voltage divider resistors (apparently where the 555 designation came from).

• When the TRIGger voltage goes below 1/3 Vcc, (and the THRS voltage is below 2/3 Vcc), the FF is Set (OUTput high and DIScharge open).
• When the THRShold voltage goes above 2/3 Vcc (and the TRIG voltage is above 1/3 Vcc), the FF is Cleared (OUT low, and DIScharge connected to ground by the transistor to discharge the timing capacitor).
• The RST (Reset) terminal Clears the FF when driven low (<0.5V). It can be connected to Vcc for normal operation.
• The CV (Control Voltage) terminal is connected between the top two resistors of the three internal 5kΩ voltage divider resistors that determine the 1/3 and 2/3 Vcc trigger points. It is typically used to add a 10nF capacitor to GND if there is a concern about Vcc noise affecting the 555 timing. It can also be used as an input to adjust the triggers points and thus the timing, for such applications as PWM (Pulse-Width-Modulation).

Below is an LTspice simulation showing the 555 TRIG level (green trace) that triggers the output high (red trace), and the THRS level (yellow trace) that triggers the output low, as noted in the first two descriptive statements above.
Also shows that the DIS pin (blue trace) goes to ground when the output is low, and goes open when the output is high.

So if you understand the above, then it should be easier to understand the operation of the 555 in it's various modes of operation, such as an astable or monostable multivibrator, or just being used as a level triggered latch.

And the timing of your traffic light circuit is determined by the time it takes to charge and discharge the 100µF timing capacitors between 1/3 and 2/3 of the supply voltage.