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%

Question

Physics

Trevin Taylor

17 March, 00:23

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%

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Answers (1)

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Laci Moreno · Answer 1

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