INDEX

In the above circuit you can see that charging will occur through Ra,Rb1,C path and discharging occurs through Rb2,C path,because during charging the diode in series with Rb2 is reverse biased and no current will flow through that path and the charging occurs through (Ra+Rb1)C and during discharging the diode in series with Rb1 is reverse biased and no current will flow through that path, thus discharge path becomes Rb2C.
Charging time = .693(Ra+Rb1)C
discharging time=.693Rb2C
Ttotal = .693(Ra+Rb1+Rb2)C
Rb1+Rb2= total resistance of variable resistor which won't change and Ra is a fixed resistor, so Ttotal = constant.