Time constants for fast RC circuits.......... Exercise 1: Two capacitors with ca

Question

Time constants for fast RC circuits..........

Exercise 1: Two capacitors with capacitance C = 10 µF are connected in series in a circuit with resistance R = 150 . What is the time constant for this circuit?

Exercise 2: What would be the value for t1/2 for the circuit above?

Exercise 3: An AC power source supplies 12 V to a circuit and oscillates with a frequency of f = 60 Hz. What will the potential of the source be 12 ms after it is turned on?

Exercise 4: What happens to the value of t1/2 when the maximum potential of the source increases?

Explanation / Answer

1. when capacitors are connected in series. then equivalent capacitance Ceq will be

1/Ceq = 1/C + 1/C = 2/C

Ceq = C/2 = 5 uF

Time constant = R Ceq = 150 x 5 x 10^-6 = 7.5 x 10^-4 s

2. Q = Q0 [ 1- e^(t/T)]

0.5Q0 = Q0 [ 1- e^(t/T)]

e^(-t/T) = 0.5

t = 0.693 T   = 0.693 x 7.5 x 10^-4 = 5.10 x 10^-4 s

3. V = Vmax sin(2pi f t)

V = 12 sin(2 x pi x 60 x 12 x 10^-3) = 12 sin(4.52)

V = - 11.787 Volt

4. t1/2 will remain same.
it only depends on time constant of circuit.

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