Find the time constants of the circuits below. Solution a)100 Ohms and 50 Ohms a

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a)100 Ohms and 50 Ohms are in series => R = 100+50 = 150 Ohms 15 mH and 10 mH are in series => L = 15+10 = 25 mH Time constant = L/R = (25/1000)/150 = 0.000166667 Seconds b)10 mH and 10 mH are in parallel => L' = (10*10)/(10+10) = 100/20 = 5 mH Then L' and 5 mH are in series => L = 5+5 = 10 mH R = 100 Ohms Therefore time constant = L/R = (10/1000)/100 = 0.0001 seconds d)1 KOhm, 4 KOhm, 1 KOhms are in series => R' = 6 KOhms Then R' and 6 KOhms are in parallel => R'' = 3 KOhms Then R'', 2 KOhms, 3 KOhms are in series => R = 2+3+3 = 8 KOhms C = 0.33 uF =>Time constant = RC = 0.33*(10^(-6))*8*(1000) = 0.00264 Seconds e)10 nF, 10 nF are in parallel => C = 20 nF 22 KOhms, 47 KOhms are in parallel => R = ((22*47)/(22+47))*1000 Ohms =>Time constant = RC = ((22*47)/(22+47))*1000*20*(10^(-9)) = 0.00029971 seconds

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