What is the time constant of a circuit with two 220-microfarad capacitors and two 1-megohm resistors in parallel?

The time constant of an RC (resistor-capacitor) circuit is calculated using the formula τ = R x C, where τ is the time constant, R is the resistance in ohms, and C is the capacitance in farads.

In this scenario, you have two 220-microfarad capacitors in parallel. When capacitors are connected in parallel, their capacitances add up. So, the total capacitance (C) is:

C = C1 + C2 = 220 µF + 220 µF = 440 µF = 440 x 10^-6 F.

You also have two 1-megohm resistors in parallel. For resistors in parallel, the total resistance (R) is calculated using the formula:

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

Substituting the resistor values:

1/R_total = 1/(1,000,000) + 1/(1,000,000)

= 2/(1,000,000)

= 2 x 10^-6.

Inverting that gives you:

R_total = 1/(2 x 10^-6) = 500,000 ohms or