For the given circuit, find vo() when (0) = 6 A and v(t) = OV. 252 v(t) i(t) 0.4 H m www 352 y (1) The voltage v₂ (t) = v(0) e-t/¹, where vo(0) = V and T =

Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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For the given circuit, find \( v_o(t) \) when \( i(0) = 6 \, \text{A} \) and \( v(t) = 0 \, \text{V} \).

**Circuit Description:**
- There is an inductor of \( 0.4 \, \text{H} \) and a resistor of \( 2 \, \Omega \) connected in series, followed by another resistor of \( 3 \, \Omega \) connected in parallel.
- The circuit includes a current source \( i(t) \) and a voltage across it \( v(t) \).
- The output voltage across the \( 3 \, \Omega \) resistor is denoted as \( v_o(t) \).

**Equation for the Output Voltage:**
\[ 
v_o(t) = v_o(0) \, e^{-t/\tau} 
\]

where \( v_o(0) = \underline{\hspace{1cm}} \, \text{V} \) and \( \tau = \underline{\hspace{1cm}} \, \text{s} \).
Transcribed Image Text:For the given circuit, find \( v_o(t) \) when \( i(0) = 6 \, \text{A} \) and \( v(t) = 0 \, \text{V} \). **Circuit Description:** - There is an inductor of \( 0.4 \, \text{H} \) and a resistor of \( 2 \, \Omega \) connected in series, followed by another resistor of \( 3 \, \Omega \) connected in parallel. - The circuit includes a current source \( i(t) \) and a voltage across it \( v(t) \). - The output voltage across the \( 3 \, \Omega \) resistor is denoted as \( v_o(t) \). **Equation for the Output Voltage:** \[ v_o(t) = v_o(0) \, e^{-t/\tau} \] where \( v_o(0) = \underline{\hspace{1cm}} \, \text{V} \) and \( \tau = \underline{\hspace{1cm}} \, \text{s} \).
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