For the given RC circuit, the capacitor is initially uncharged.At t=0: S1, S2, and S3 are closed.At t=1ms: S1 is open, but S2 & S3 are kept close. Find the voltage Vout at t=2ms E=1V, R=1k ohm, C=2uF.Select one:a. 0.37 Vb. 0.865V c. none of the answersd. 1.865 Ve. 1 V
Question
For the given RC circuit, the capacitor is initially uncharged.At t=0: S1, S2, and S3 are closed.At t=1ms: S1 is open, but S2 & S3 are kept close. Find the voltage Vout at t=2ms E=1V, R=1k ohm, C=2uF.Select one:a. 0.37 Vb. 0.865V c. none of the answersd. 1.865 Ve. 1 V
Solution
The voltage across a charging capacitor in an RC circuit is given by the formula:
V(t) = V0 * (1 - e^(-t/RC))
where:
- V(t) is the voltage across the capacitor at time t,
- V0 is the initial voltage across the capacitor (which is 0V in this case since the capacitor is initially uncharged),
- R is the resistance,
- C is the capacitance,
- e is the base of the natural logarithm (approximately 2.71828),
- t is the time elapsed since the start of charging.
Given that E=1V, R=1k ohm, C=2uF, and t=2ms - 1ms = 1ms (since S1 is opened at t=1ms), we can substitute these values into the formula to find Vout:
Vout = 1V * (1 - e^(-1ms / (1k ohm * 2uF)))
This simplifies to:
Vout = 1V * (1 - e^(-1))
Using a calculator to evaluate e^(-1) gives approximately 0.36788. Subtracting this from 1 gives:
Vout = 1V * (1 - 0.36788) = 0.632V
However, this answer is not listed in the options. Therefore, the correct answer is:
c. none of the answers
Similar Questions
For the given RC circuit, the capacitor is initially uncharged.At t=0: S1, S2, and S3 are closed.At t=1ms: S1 is open, but S2 & S3 are kept close. Find the voltage Vout at t=2ms E=1V, R=1k ohm, C=2uF.Select one:a. 0.37 Vb. 0.865V c. none of the answersd. 1.865 Ve. 1 V
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