In, suppose that & = 50.0 V, R=240.0 2 and L = 0.170 H. With switch S₂ open, switch S₁ is left closed until a constant current is established. Then S₂ is closed and S₁ opened, taking the battery out of the circuit. Part A What is the initial current in the resistor, just after S2 is closed and S₁ is opened? Express your answer in amperes. R

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### Educational Exercise on Circuit Analysis

**Problem Statement:**

In the given circuit, assume the following parameters:
- Electromotive force, \( \mathcal{E} = 50.0 \, \text{V} \)
- Resistance, \( R = 240.0 \, \Omega \)
- Inductance, \( L = 0.170 \, \text{H} \)

Initially, with switch \( S_2 \) open, switch \( S_1 \) is closed until a constant current is established. Then, \( S_2 \) is closed and \( S_1 \) is opened, removing the battery from the circuit. 

**Circuit Diagram Explanation:**

The circuit diagram features:
- A battery of electromotive force \( \mathcal{E} \).
- A resistor labeled \( R \).
- An inductor labeled \( L \).
- Two switches, \( S_1 \) and \( S_2 \), control the flow of current in the circuit path.

The circuit forms a simple RL circuit when \( S_1 \) is opened and \( S_2 \) is closed. The current \( i \) flows through the resistor \( R \) and inductor \( L \).

**Questions:**

**Part A:**

*Question:* What is the initial current in the resistor just after \( S_2 \) is closed and \( S_1 \) is opened?

*Answer Format:* Express your answer in amperes.

\[ I = \_\_\_\_ \, \text{A} \]

**Part B:**

*Question:* What is the current in the resistor at \( t = 4.20 \times 10^{-4} \) s?

*Answer Format:* Express your answer in amperes.

\[ I = \_\_\_\_ \, \text{A} \]

Participants are encouraged to express answers using appropriate equations for RL circuits and consider the effects of the inductor on current change over time as it resists changes in current.
Transcribed Image Text:### Educational Exercise on Circuit Analysis **Problem Statement:** In the given circuit, assume the following parameters: - Electromotive force, \( \mathcal{E} = 50.0 \, \text{V} \) - Resistance, \( R = 240.0 \, \Omega \) - Inductance, \( L = 0.170 \, \text{H} \) Initially, with switch \( S_2 \) open, switch \( S_1 \) is closed until a constant current is established. Then, \( S_2 \) is closed and \( S_1 \) is opened, removing the battery from the circuit. **Circuit Diagram Explanation:** The circuit diagram features: - A battery of electromotive force \( \mathcal{E} \). - A resistor labeled \( R \). - An inductor labeled \( L \). - Two switches, \( S_1 \) and \( S_2 \), control the flow of current in the circuit path. The circuit forms a simple RL circuit when \( S_1 \) is opened and \( S_2 \) is closed. The current \( i \) flows through the resistor \( R \) and inductor \( L \). **Questions:** **Part A:** *Question:* What is the initial current in the resistor just after \( S_2 \) is closed and \( S_1 \) is opened? *Answer Format:* Express your answer in amperes. \[ I = \_\_\_\_ \, \text{A} \] **Part B:** *Question:* What is the current in the resistor at \( t = 4.20 \times 10^{-4} \) s? *Answer Format:* Express your answer in amperes. \[ I = \_\_\_\_ \, \text{A} \] Participants are encouraged to express answers using appropriate equations for RL circuits and consider the effects of the inductor on current change over time as it resists changes in current.
**Part C**

What is the potential difference between points b and c at \( t = 4.20 \times 10^{-4} \, \text{s} \)?

*Express your answer in volts.*

\[ V = \] [Input box for answer] \(\text{V}\)

- [Submit Button]
- [Request Answer Button]

---

**Part D**

Which point is at a higher potential?

- [ ] b
- [ ] c

- [Submit Button]
- [Request Answer Button]

---

**Part E**

How long does it take the current to decrease to half its initial value?

*Express your answer in seconds.*

\[ t = \] [Input box for answer] \(\text{s}\)

- [Submit Button]
- [Request Answer Button]
Transcribed Image Text:**Part C** What is the potential difference between points b and c at \( t = 4.20 \times 10^{-4} \, \text{s} \)? *Express your answer in volts.* \[ V = \] [Input box for answer] \(\text{V}\) - [Submit Button] - [Request Answer Button] --- **Part D** Which point is at a higher potential? - [ ] b - [ ] c - [Submit Button] - [Request Answer Button] --- **Part E** How long does it take the current to decrease to half its initial value? *Express your answer in seconds.* \[ t = \] [Input box for answer] \(\text{s}\) - [Submit Button] - [Request Answer Button]
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