Assume the switch is closed and enough time has elapsed for the circuit to be in "steady-state,"and the components are ideal. Find the value of V1 for the circuit below. Merely write the number; the answer is understood to be in volts 12 V 100 µF 2 H v, 4 2

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**Question 10**

Assume the switch is closed and enough time has elapsed for the circuit to be in **steady-state,** and the components are ideal. Find the value of \( V_1 \) for the circuit below. Merely write the number; the answer is understood to be in volts.

**Circuit Description:**

The circuit includes the following components:

1. A 12 V DC voltage source connected to a switch.
2. An 8 Ω resistor in series with the voltage source.
3. A parallel branch with:
   - A 2 H inductor and a 4 Ω resistor in series, with a voltage across the resistor labeled \( V_1 \).
   - A 100 µF capacitor in series with an 8 Ω resistor, with a voltage across the resistor labeled \( V_2 \).

**Analysis:**

- In a steady-state condition, the inductor acts as a short circuit, and the capacitor acts as an open circuit.
- For the left branch (with the inductor and resistor), the current \( I_1 \) flows through the 4 Ω resistor.
- In the right branch, there is no current through the capacitor, and only \( I_2 \) flows through the 8 Ω resistor.

The task is to find \( V_1 \), the voltage across the 4 Ω resistor in the left branch when the circuit reaches steady state.
Transcribed Image Text:**Question 10** Assume the switch is closed and enough time has elapsed for the circuit to be in **steady-state,** and the components are ideal. Find the value of \( V_1 \) for the circuit below. Merely write the number; the answer is understood to be in volts. **Circuit Description:** The circuit includes the following components: 1. A 12 V DC voltage source connected to a switch. 2. An 8 Ω resistor in series with the voltage source. 3. A parallel branch with: - A 2 H inductor and a 4 Ω resistor in series, with a voltage across the resistor labeled \( V_1 \). - A 100 µF capacitor in series with an 8 Ω resistor, with a voltage across the resistor labeled \( V_2 \). **Analysis:** - In a steady-state condition, the inductor acts as a short circuit, and the capacitor acts as an open circuit. - For the left branch (with the inductor and resistor), the current \( I_1 \) flows through the 4 Ω resistor. - In the right branch, there is no current through the capacitor, and only \( I_2 \) flows through the 8 Ω resistor. The task is to find \( V_1 \), the voltage across the 4 Ω resistor in the left branch when the circuit reaches steady state.
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