Subelement B: Electrical Math— Topic 15: RC Time Constants-2
Question 3-15B5
Element 3 (GROL)What is the time constant of a circuit having two 100-microfarad capacitors and two 470-kilohm resistors all in parallel?
Explanation
The time constant (τ) of a resistor-capacitor (RC) circuit is calculated by the formula τ = RC, where R is the total resistance and C is the total capacitance.
First, determine the total capacitance. When capacitors are connected in parallel, their capacitances add together:
C_total = 100 µF + 100 µF = 200 µF.
Next, determine the total resistance. When identical resistors are connected in parallel, their equivalent resistance is half the value of a single resistor:
R_total = 470 kΩ / 2 = 235 kΩ.
Now, calculate the time constant using the total resistance and capacitance:
τ = R_total × C_total
τ = 235 kΩ × 200 µF
To ensure the answer is in seconds, convert kilohms to ohms (× 10^3) and microfarads to farads (× 10^-6):
τ = (235 × 10^3 Ω) × (200 × 10^-6 F)
τ = 47,000 × 10^-3 seconds
τ = 47 seconds.
Therefore, the time constant is 47 seconds. Options A, C, and D are incorrect as they do not account for the proper combination of parallel components or unit conversions.
Related Questions
3-15B3 What is the time constant of a circuit having a 100-microfarad capacitor and a 470-kilohm resistor in series?3-15B4 What is the time constant of a circuit having a 220-microfarad capacitor and a 1-megohm resistor in parallel?3-15B6 What is the time constant of a circuit having two 220-microfarad capacitors and two 1-megohm resistors all in series?3-16B1 What is the impedance of a network composed of a 0.1-microhenry inductor in series with a 20-ohm resistor, at 30 MHz? Specify your answer in rectangular coordinates.3-16B2 In rectangular coordinates, what is the impedance of a network composed of a 0.1-microhenry inductor in series with a 30-ohm resistor, at 5 MHz?