Question

it is rc time constant problem.

1.

Solve the equation for a charging capacitor (V_c = V_s(1-e^(t/t))) for an RC Circuit for the ratio of the time (t) to the RC time constant (t):

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2.

Using the answer to Part 1, calculate the fraction of a time constant (t) to charge an initially uncharged capacitor to 10% of the source voltage (V_s).

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3.

Using the appropriate answers from Part 1, calculate the fraction of a time constant (t) required to charge an initially uncharged first 10% (0% - 10%) of the maximum circuit voltage (V_s).

4.

Using the appropriate answers from Part 1, calculate the number of time constants (t) required to charge an initially uncharged last 10% (90% - 99%) of the maximum circuit voltage (V_s).

Answer 1

2.

When the capacitor volatage is 10% of the source voltage then , so,

(ans)

3. As the conditions are the same as part 2 so the answer is same too. 0.1053 of time constant.

4.

Time takes in terms of the number of time costant to reach 90% of the mamximum voltage =

time constants.

And to reach from nothing to 99% of the mamximum voltage it takes,

time constants,

So from 90% to 99% it takes, 4.6-2.3 = 2.3 time constants.