QUIZ: CHARGING TIME OF A CAPACITOR

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Determine R to charge the capacitor in 1 second.

Let us assume that we have the following circuit, starting from a discharged capacitor with a capacity of 100 microFarads and connected to a battery by means of a resistor R. We want to determine the value of the resistor R which allows the capacitor to be charged in about 1 second.

SOLUTION

The theory tells us that the charge of the capacitor depends on the time constant of the circuit which is equal to the product 𝑅 ∙ 𝐶 where R must be expressed in Ohm and C in Farad.

The theory also tells us that the capacitor charge exceeds 99% after 5 time constants:

Charge>99%=5 ∙Time constant

We must therefore ensure that:

5∙R∙C=1 second

From which we can determine R:

R=1/(5∙C)=1/(5∙100μF)=1/(5∙10^(-4) )=2000 Ω

And therefore, the resistor to be inserted in the circuit must have a resistance equal to 2000 Ω or equivalently 2 kΩ.

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