What is the time constant of a circuit with two 100-microfarad capacitors and two 470-kilohm resistors in series?

To determine the time constant of a circuit that includes capacitors and resistors, it's essential to understand how to calculate the time constant (τ) for an RC (resistor-capacitor) circuit. The time constant is given by the formula τ = R × C, where R is the resistance in ohms and C is the capacitance in farads.

In this case, you have two 100-microfarad capacitors in series, which means the total capacitance (C) is calculated as:

1/C_total = 1/C1 + 1/C2

1/C_total = 1/(100 × 10⁻⁶) + 1/(100 × 10⁻⁶)

1/C_total = 2/(100 × 10⁻⁶)

C_total = 50 microfarads = 50 × 10⁻⁶ farads

For the resistors, having two 470-kilohm resistors in series means the total resistance (R) is simply the sum of the resistances:

R = R1 + R2

R = 470,000 + 470,000 ohms

R = 940,000 ohms

Now,