Determine v.(f) for t>0. Let i, 10 u(t) HA and assume that the capacitor is initially uncharged. 10 k2 2 µF ww ww 50 k2 i, Also, find the capacitor voltage as a function of time.

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ISBN:9780133923605
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**Chapter 7, Problem 74**

**Task:**
Determine \( v_o(t) \) for \( t > 0 \). Let \( i_s = 10 \, u(t) \, \mu A \) and assume that the capacitor is initially uncharged.

**Diagram Description:**

The circuit consists of the following components:

- A current source \( i_s \) defined as \( 10 \, u(t) \, \mu A \).
- A 50 kΩ resistor connected in series with the current source.
- A 2 μF capacitor parallel to the 50 kΩ resistor.
- An operational amplifier (op-amp) with its inverting input connected to the junction between the 50 kΩ resistor and the capacitor.
- A 10 kΩ resistor connected from the output of the op-amp to its inverting input.
- The output voltage of the op-amp is labeled \( v_o \).
- The non-inverting input of the op-amp is grounded.

**Objective:**

Find \( v_o(t) \) and the capacitor voltage as functions of time. 

Given the initial conditions, there are opportunities to apply the properties of ideal op-amps, differential equations in RLC circuits, and step response analysis to solve the problem.
Transcribed Image Text:**Chapter 7, Problem 74** **Task:** Determine \( v_o(t) \) for \( t > 0 \). Let \( i_s = 10 \, u(t) \, \mu A \) and assume that the capacitor is initially uncharged. **Diagram Description:** The circuit consists of the following components: - A current source \( i_s \) defined as \( 10 \, u(t) \, \mu A \). - A 50 kΩ resistor connected in series with the current source. - A 2 μF capacitor parallel to the 50 kΩ resistor. - An operational amplifier (op-amp) with its inverting input connected to the junction between the 50 kΩ resistor and the capacitor. - A 10 kΩ resistor connected from the output of the op-amp to its inverting input. - The output voltage of the op-amp is labeled \( v_o \). - The non-inverting input of the op-amp is grounded. **Objective:** Find \( v_o(t) \) and the capacitor voltage as functions of time. Given the initial conditions, there are opportunities to apply the properties of ideal op-amps, differential equations in RLC circuits, and step response analysis to solve the problem.
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