Question

A 0.1 cm 2 electrode with Сд = 20 /xF/cm2 is subjected to a potential step under conditions where Rs is 1, 10, or 100 ft. In each case, what is the time constant, and what is the time required for the dou ble-layer charging to be 95% complete?

Answer 1

The time constant for double-layer charging is given by:

τ = Cd * Rs
where:

Cd is the double-layer capacitance (/xF/cm2)
Rs is the solution resistance (ft)
In this case, Cd = 20 /xF/cm2 and Rs = 1, 10, or 100 ft. So, the time constants are:

Rs = 1 ft: τ = 20 * 1 = 20 s
Rs = 10 ft: τ = 20 * 10 = 200 s
Rs = 100 ft: τ = 20 * 100 = 2000 s
The time required for the double-layer charging to be 95% complete is given by:

t = 3 * τ
So, the times required for the double-layer charging to be 95% complete are:

Rs = 1 ft: t = 3 * 20 = 60 s
Rs = 10 ft: t = 3 * 200 = 600 s
Rs = 100 ft: t = 3 * 2000 = 6000 s