Answered: The figure shows an LR circuit with L =… | bartleby

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The figure shows an LR circuit with L = 0.15 H, R = 25 Ω, and Vo = 36 V. The switch is initially open. Eight milliseconds (t = 8 ms) after the switch is closed, what is the current in the circuit and the potential difference between points a and b, V_ab ?

### Basic RL Circuit Analysis

#### Introduction

An RL circuit is a type of electric circuit that consists of both a resistor (R) and an inductor (L) connected in series with a voltage source (V₀). This type of circuit is commonly used in various electronic applications, including filtering, tuning, and in signal processing.

#### RL Circuit Diagram

The diagram above represents a simple RL circuit. It includes the following components:

1. **Voltage Source (V₀):** This provides the driving voltage for the circuit.
2. **Resistor (R):** Represents an element that resists the flow of electric current, dissipating energy as heat.
3. **Inductor (L):** Represents an element that resists changes in current. It stores energy in a magnetic field when current flows through it.
4. **Switch (S):** A component that can open or close the circuit.

#### Diagram Explanation

- **Components and Connections:**
- **Voltage Source (V₀)**: The voltage source is positioned on the left side of the circuit diagram. It supplies the necessary electric potential to drive the current through the circuit.
- **Resistor (R)**: The resistor is connected in series with the voltage source at the top.
- **Inductor (L)**: The inductor is also connected in series with the resistor and completes the circuit by connecting to the bottom terminal.
- **Switch (S)**: The switch, located at the bottom left of the circuit, allows for opening or closing the circuit to control the flow of current through the resistor and inductor.

- **Nodes:**
- **Node a**: The connection point between the resistor and inductor.
- **Node b**: The connection point below the inductor and near the switch.

#### Functioning of the RL Circuit:

When the switch is closed at t=0, the voltage source V₀ begins to apply a potential difference across the resistor and inductor. The inductor initially resists the change in current through it, causing a gradual increase in the current flow over time. The current in the circuit eventually reaches a steady state, where the inductor behaves like a short circuit, and the only significant element resisting the current is the resistor.

#### Mathematical Analysis:
The behavior of the current \( I(t) \) in the circuit can be described by the following differential equation:

\[ V_0 = L \frac{

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