In the transient shown the time constant of the circuit is :
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Applying Thevenin's theorem we consider the circuit from right side and short circuiting the voltage sources and opening the extreme right resistance we get the equivalent resistance
$=\frac{1}{R_{t h}}=\frac{1}{3 R}+\frac{1}{R}=\frac{4}{3 R}=\frac{3 R}{4} R_{t h}=$ Thevenins resistance
So now adding the remaining resistance $\mathrm{R}$ with $R_{t h}$ in series we get the equivalent resistance
$R_{e q}=\frac{3 R}{4}+R=\frac{7 R}{4}$
And time constant $\tau=\mathrm{RC}$
$\tau=\frac{7}{4} \mathrm{RC}$
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