Question 3-15B1

The time constant ($\tau$) of an RC circuit is calculated by multiplying the total resistance (R) by the total capacitance (C): $\tau = RC$. First, determine the equivalent resistance ($R_{eq}$) of the two 1-megohm resistors in parallel. For two identical resistors in parallel, $R_{eq} = R/2$. So, $R_{eq} = 1 \text{ M}\Omega / 2 = 0.5 \text{ M}\Omega$, or $500,000 \, \Omega$. Next, determine the equivalent capacitance ($C_{eq}$) of the two 220-microfarad capacitors in parallel. For capacitors in parallel, you add their values: $C_{eq} = C_1 + C_2$. So, $C_{eq} = 220 \, \mu F + 220 \, \mu F = 440 \, \mu F$, or $440 \times 10^{-6} \, F$. Finally, calculate the time constant: $\tau = R_{eq} \times C_{eq}$ $\tau = 500,000 \, \Omega \times 440 \times 10^{-6} \, F$ $\tau = 220 \, \text{seconds}$ Incorrect options would result from errors in calculating equivalent resistance, equivalent capacitance, or the final multiplication. For instance, using 1 MΩ for resistance or 220 µF for capacitance would lead to different incorrect answers.