For the circuit shown above, determine the following: i. Complete the auxillary equation for the differential equation for i(t) for t>0? 1.25s2+ =0 ii. What is the current in the inductor before the switch is opened? iii. What is the magnitude of the voltage across the capacitor just before the switch is opened)?

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For the circuit shown above, determine the following:

i. Complete the auxiliary equation for the differential equation for \(i(t)\) for \(t>0\)?
\[ 1.25s^2 + \_\_\_\_ = 0 \]

ii. What is the current in the inductor before the switch is opened?
\[ \_\_\_\_ \, \text{A} \]

iii. What is the magnitude of the voltage across the capacitor just before the switch is opened?
\[ \_\_\_\_ \, \text{V} \]
Transcribed Image Text:For the circuit shown above, determine the following: i. Complete the auxiliary equation for the differential equation for \(i(t)\) for \(t>0\)? \[ 1.25s^2 + \_\_\_\_ = 0 \] ii. What is the current in the inductor before the switch is opened? \[ \_\_\_\_ \, \text{A} \] iii. What is the magnitude of the voltage across the capacitor just before the switch is opened? \[ \_\_\_\_ \, \text{V} \]
The diagram represents an electrical circuit containing various components. Here's a detailed explanation:

**Components and Configuration:**

1. **Voltage Sources:**
   - A 12V voltage source on the left side.
   - A 6V voltage source in the middle of the circuit.

2. **Resistors:**
   - A 6Ω resistor is connected in series with the top path of the circuit.
   - A 1.5Ω resistor is connected in series with the right path of the circuit.

3. **Inductor:**
   - A 1.25 H inductor is placed in the path with the 12V source.

4. **Capacitor:**
   - A 0.1 F capacitor is connected in the branch with the 1.5Ω resistor.

5. **Switch:**
   - A switch is located between the paths containing the resistors and is initially open (indicated by \( t = 0 \)). Its direction is curved towards the 1.5Ω resistor.

6. **Current:**
   - The current \( i(t) \) is marked on the left path, suggesting it flows through the 12V source and the inductor.

**Circuit Analysis:**

- This circuit appears to be suited for transient analysis at the moment when the switch is closed (\( t = 0 \)).
- The combination of resistors, inductor, and capacitor indicates that this could be an RLC circuit, often used to demonstrate the behavior of reactive components in AC and transient states.

By analyzing this setup, one can explore concepts such as time constants, reactive behavior, energy storage, and dissipation in electrical circuits.
Transcribed Image Text:The diagram represents an electrical circuit containing various components. Here's a detailed explanation: **Components and Configuration:** 1. **Voltage Sources:** - A 12V voltage source on the left side. - A 6V voltage source in the middle of the circuit. 2. **Resistors:** - A 6Ω resistor is connected in series with the top path of the circuit. - A 1.5Ω resistor is connected in series with the right path of the circuit. 3. **Inductor:** - A 1.25 H inductor is placed in the path with the 12V source. 4. **Capacitor:** - A 0.1 F capacitor is connected in the branch with the 1.5Ω resistor. 5. **Switch:** - A switch is located between the paths containing the resistors and is initially open (indicated by \( t = 0 \)). Its direction is curved towards the 1.5Ω resistor. 6. **Current:** - The current \( i(t) \) is marked on the left path, suggesting it flows through the 12V source and the inductor. **Circuit Analysis:** - This circuit appears to be suited for transient analysis at the moment when the switch is closed (\( t = 0 \)). - The combination of resistors, inductor, and capacitor indicates that this could be an RLC circuit, often used to demonstrate the behavior of reactive components in AC and transient states. By analyzing this setup, one can explore concepts such as time constants, reactive behavior, energy storage, and dissipation in electrical circuits.
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