Given, array ll R₁=1 & C₁=2 ~F R₂=2 & C₂=4 ~F array The time constant (in s ) for the circuits I, II, III are respectively

Step-by-step solution

For (I): The net capacitance ( C = C ₁ C ₂ C ₁+ C ₂ = 2 4 2+4 =4 / 3 ~F ) and net resistance ( R = R ₁ R ₂ R ₁+ R ₂ = 1 2 1+2 =2 / 3 ) Thus, time constant ( = CR =(4 / 3)(2 / 3)=(8 / 9) S ) For (II): ( C = C ₁+ C ₂=2+4=6 ~F ) and ( R = R ₁+ R ₂=1+2=3 ) Thus, time constant ( = CR =(6)(3)=18 ~S ) For (III): ( C = C ₁+ C ₂=2+4=6 ~F ) and ( R = R ₁ R ₂ R ₁+ R ₂ =2 / 3 ) Thus, time constant ( = CR =(6)(2 / 3)=4 ~S )