Please show all calculations. (1) If a circuit is using two 2 µF capacitors conn
ID: 1442322 • Letter: P
Question
Please show all calculations.
(1) If a circuit is using two 2 µF capacitors connected in series, what is the total capacitance of the circuit?
(2) Consider an RC circuit with a time constant of 1 ms. The capacitor has a value of 10 µF. What is the value of the resistor in this circuit? To lengthen the time constant would the resistance value have to be raised or lowered?
(3) The time constant for one RC circuit is known to be 1.2 seconds (we will call this the first RC circuit). A second RC circuit is known to have a time constant of 3.6 seconds. Initially, the two capacitors are fully charged and both circuits have open switches. The circuits are then closed and the capacitors are discharged until they have one-fourth of their original charge. Which of the following is true?
(A) The first RC circuit takes one-third as long to complete this process as the second.
(B)The first RC circuit takes three times as long to complete this process as the second.
(C) The first RC circuit takes one-fourth as long to complete this process as the second.
(D) The first RC circuit takes four times as long to complete this process as the second.
(E) The first RC circuit takes 2.4 seconds longer to compete this process than the second.
(A) The first RC circuit takes one-third as long to complete this process as the second.
(B)The first RC circuit takes three times as long to complete this process as the second.
(C) The first RC circuit takes one-fourth as long to complete this process as the second.
(D) The first RC circuit takes four times as long to complete this process as the second.
(E) The first RC circuit takes 2.4 seconds longer to compete this process than the second.
Explanation / Answer
1) total capacitance = 2×2/(2+2) = 1 uF
2)R = time constant / Capacitor = 0.001/(10 × 10^-6) = 0.001/ 0.00001 = 100 ohms
To lengthen time constant, R has to be increased
3)A option is correct because time constant of first is one-third of second
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