Question
What is the time constant of a circuit having two 220-microfarad capacitors and two 1-megohm resistors, all in parallel?
Answer Options
- A) 55 seconds
- B) 110 seconds
- C) 440 seconds
- D) 220 seconds
Correct Answer: D
Explanation
The time constant (\tau) of an RC circuit is calculated as \tau = R \times C. When components are connected in parallel, their total equivalent resistance (R_{EQ}) and capacitance (C_{EQ}) must first be calculated before finding the time constant. The reciprocal formula is used for parallel resistors, while parallel capacitance is additive.
In this case, the total capacitance is C_{EQ} = C_1 + C_2 = 220 \mu F + 220 \mu F = 440 \mu F. The total resistance is R_{EQ} = \frac{R_1 \times R_2}{R_1 + R_2} = \frac{1 \text{ M}\Omega \times 1 \text{ M}\Omega}{1 \text{ M}\Omega + 1 \text{ M}\Omega} = 0.5 \text{ M}\Omega. The time constant is then \tau = R_{EQ} \times C_{EQ} = (0.5 \times 10^6 \Omega) \times (440 \times 10^{-6} \text{ F}) = 220 \text{ seconds}.
This topic was automatically created to facilitate community discussion about this exam question. Feel free to share study tips, memory tricks, or additional explanations!