Problem 42 t = Os it opens instantaneously. Assuming ß = 50, find: The switch in the following circuit has been closed for a long time. At a) the capacitor voltage v(t) for t < 0 assuming DC conditions. b) the capacitor voltage v(t) for t > 0. c) How many milliseconds after the switch opens is the capacitor voltage 36% of its final value?

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**Problem 4:**

The switch in the following circuit has been closed for a long time. At \( t = 0 \)s it opens instantaneously. Assuming \( \beta = 50 \), find:

a) The capacitor voltage \( v(t) \) for \( t < 0 \) assuming DC conditions.

b) The capacitor voltage \( v(t) \) for \( t > 0 \).

c) How many milliseconds after the switch opens is the capacitor voltage 36% of its final value?

**Circuit Description:**

- The circuit features a current source of \( 120 \, \mu\text{A} \).
- There is a \( 33 \, \text{k}\Omega \) resistor and a \( 47 \, \text{k}\Omega \) resistor in series with the closed switch at \( t = 0 \).
- A dependent current source, \( \beta i_b \), is present, where \( \beta = 50 \).
- The dependent source is connected in parallel with a \( 16 \, \text{k}\Omega \) resistor and a \( 0.25 \, \mu\text{F} \) capacitor.
- The voltage across the capacitor is denoted as \( v \).

This configuration helps in analyzing the response of the capacitor voltage over time with respect to the switch's action and the dependent source’s influence.
Transcribed Image Text:**Problem 4:** The switch in the following circuit has been closed for a long time. At \( t = 0 \)s it opens instantaneously. Assuming \( \beta = 50 \), find: a) The capacitor voltage \( v(t) \) for \( t < 0 \) assuming DC conditions. b) The capacitor voltage \( v(t) \) for \( t > 0 \). c) How many milliseconds after the switch opens is the capacitor voltage 36% of its final value? **Circuit Description:** - The circuit features a current source of \( 120 \, \mu\text{A} \). - There is a \( 33 \, \text{k}\Omega \) resistor and a \( 47 \, \text{k}\Omega \) resistor in series with the closed switch at \( t = 0 \). - A dependent current source, \( \beta i_b \), is present, where \( \beta = 50 \). - The dependent source is connected in parallel with a \( 16 \, \text{k}\Omega \) resistor and a \( 0.25 \, \mu\text{F} \) capacitor. - The voltage across the capacitor is denoted as \( v \). This configuration helps in analyzing the response of the capacitor voltage over time with respect to the switch's action and the dependent source’s influence.
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