Question

What multiple of the time constant τ gives the time taken by an initially uncharged capacitor in an RC series circuit to be charged to 94.5% of its final charge? Number Enter your answer in accordance to the question statement Units Choose the answer from the menu in accordance to the question statement the tolerance is +/-2%

Answer 1

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