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Four identical capacitors are connected with a resistor in two different ways. When they are connected as in part a of the drawing, the time constant to charge up this circuit is 1.48 s. What is the time constant when they are connected with the same resistor, as in part b
Four identical capacitors are connected with a resistor in two different ways. When they are connected as in part a of the drawing, the time constant to charge up this circuit is 1.48 s. What is the time constant when they are connected with the same resistor, as in part b
Answer:Explanation:GivenSee attachment for connectionRequiredDetermine the time constant in (b)First, we calculate the total capacitance (C1) in (a):The upper two connections are connected serially:So, we have:Take LCMCross MultiplyMakethe subjectThe bottom two are also connected serially.In other words, the upper and the bottom have the same capacitance.So, the total (C) is:The total capacitance in (b) is calculated as:First, we calculate the parallel capacitance (Cp) is:So, the total capacitance (C2) is:Take LCMInverse both sidesBoth (a) and (b) have the same resistance.So:We have:Time constant is directional proportional to capacitance:So:Convert to equationMake k the subjectMake T2 the subjectSubstitute values for T1, C1 and C2Hence, the time constance of (b) is 0.592 s...