Identify the differential equation for the voltage v() in the circuit shown in the given figure for time t> 0 and A= 10. Find an expression for the current i(t) for time t> 0. R, = 2 Q i,(1) C = 3 F i(t) V.(t) V,= AVE t = 0 R, = 62 The current i() is

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Identify the differential equation for the voltage \( v_C(t) \) in the circuit shown in the given figure for time \( t > 0 \) and \( A = 10 \). Find an expression for the current \( i(t) \) for time \( t > 0 \).

**Diagram Explanation:**

The circuit consists of:
- A voltage source \( V_s = A V \).
- Two resistors: \( R_1 = 2 \, \Omega \) and \( R_2 = 6 \, \Omega \).
- A capacitor \( C = 3 \, \text{F} \).
- Currents labeled as \( i_s(t) \), \( i_C(t) \), and \( i(t) \).
- A switch that is closed at \( t = 0 \).
- The voltage across the capacitor is marked as \( v_C(t) \).

**Expression to find:**

The current \( i(t) \) is \( \underline{\quad} + \underline{\quad} e^{\underline{\quad} t} \).
Transcribed Image Text:Identify the differential equation for the voltage \( v_C(t) \) in the circuit shown in the given figure for time \( t > 0 \) and \( A = 10 \). Find an expression for the current \( i(t) \) for time \( t > 0 \). **Diagram Explanation:** The circuit consists of: - A voltage source \( V_s = A V \). - Two resistors: \( R_1 = 2 \, \Omega \) and \( R_2 = 6 \, \Omega \). - A capacitor \( C = 3 \, \text{F} \). - Currents labeled as \( i_s(t) \), \( i_C(t) \), and \( i(t) \). - A switch that is closed at \( t = 0 \). - The voltage across the capacitor is marked as \( v_C(t) \). **Expression to find:** The current \( i(t) \) is \( \underline{\quad} + \underline{\quad} e^{\underline{\quad} t} \).
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