Answer:
t / τ₀ = 2.9
the time constant has to be multiplied by approximately three
Explanation:
The expression for long of a capacitor is
q = q₀ (1- e (-t/τ₀)
Where q is the charge and τ₀ is the time constant. What is found for when the initial capacitor charge at 63.5% (e⁻¹) of the maximum charge
In our case we are asked that the load be 94.5%, this means that
q/q₀ = 94.5%
q/q₀ = 0.945
Let's replace and calculate
q/q₀ = 1 - e (-t/τ₀)
0.945 = 1 - e (-t/τ₀)
(-t /τ₀) = ln (1 -0.945) = ln (0.055)
t / τ₀ = 2.9
the time constant has to be multiplied by approximately three for this charge
