For the circuit given in the figure below find v(t) and i(t) for all t.

Introductory Circuit Analysis (13th Edition)
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Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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**Problem 3**

For the circuit given in the figure below, find \( v(t) \) and \( i(t) \) for all \( t \).

**Circuit Description:**

- A voltage source of 3 V is connected in series with the components.
- There is a resistor with a resistance of \( \frac{5}{8} \, \Omega \).
- A capacitor with a capacitance of \( \frac{1}{5} \, \text{F} \).
- An inductor with an inductance of \( \frac{1}{5} \, \text{H} \).
- A switch is present, initially open at \( t = 0 \), which controls the circuit.
- The current \( i \) is shown flowing clockwise from the inductor back towards the voltage source. 

The task is to determine the expressions for the voltage \( v(t) \) across the components and the current \( i(t) \) in the circuit for all time \( t \).
Transcribed Image Text:**Problem 3** For the circuit given in the figure below, find \( v(t) \) and \( i(t) \) for all \( t \). **Circuit Description:** - A voltage source of 3 V is connected in series with the components. - There is a resistor with a resistance of \( \frac{5}{8} \, \Omega \). - A capacitor with a capacitance of \( \frac{1}{5} \, \text{F} \). - An inductor with an inductance of \( \frac{1}{5} \, \text{H} \). - A switch is present, initially open at \( t = 0 \), which controls the circuit. - The current \( i \) is shown flowing clockwise from the inductor back towards the voltage source. The task is to determine the expressions for the voltage \( v(t) \) across the components and the current \( i(t) \) in the circuit for all time \( t \).
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