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

To determine the time constant of a circuit that includes capacitors and resistors, it's essential to first understand how these components behave in combination. The time constant (τ) of an RC (resistor-capacitor) circuit is given by the formula:

τ = R_total * C_total

Where:

• R_total is the equivalent resistance in ohms,

• C_total is the equivalent capacitance in farads.

In the scenario described, you have two 100-microfarad capacitors in parallel. When capacitors are in parallel, their capacitances add together:

C_total = C1 + C2 = 100 μF + 100 μF = 200 μF = 200 x 10^-6 F = 0.0002 F.

Next, we evaluate the resistance. There are two 470-kilohm resistors connected in parallel. To find the equivalent resistance for resistors in parallel, you can use the formula:

1/R_total = 1/R1 + 1/R2.

Substituting the resistor values, we get:

1/R_total = 1/(470,000) + 1/(470,000) = 2/(470,000).

So, R_total