An inductor with inductance L = 0.400 H and negligible resistance is connected to a battery, a switch S, and two resistors, R1 = 11.0 N and R2 = 15.0 N (Figure 1). The battery has emf 96.0 V and negligible internal resistance. S is closed at t = 0 Part H When iz has half of its final value, what is i2? Express your answer with the appropriate units. HẢ i2 = Value Units Part I Figure < 1 of 1> When iz has half of its final value, what is i ? Express your answer with the appropriate units. HẢ R2 R1 i = Value Units

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### Educational Content: Inductor Circuit Analysis

An inductor with an inductance \( L = 0.400 \, \text{H} \) and negligible resistance is connected to a battery, a switch \( S \), and two resistors, \( R_1 = 11.0 \, \Omega \) and \( R_2 = 15.0 \, \Omega \), as shown in Figure 1. The battery has an electromotive force (emf) of 96.0 V and negligible internal resistance. The switch \( S \) is closed at time \( t = 0 \).

#### Circuit Diagram (Figure 1)

- The circuit consists of the following components:
  - A battery \( \mathcal{E} \) providing a voltage of 96.0 V.
  - A switch \( S \), initially open, is closed at time \( t = 0 \).
  - A resistor \( R_1 = 11.0 \, \Omega \) with current \( i_2 \) flowing through it.
  - A resistor \( R_2 = 15.0 \, \Omega \) in series with an inductor with current \( i_3 \) flowing through this branch.
  - An inductor \( L = 0.400 \, \text{H} \).
  - Three currents: \( i_1 \), \( i_2 \), and \( i_3 \).

### Problem Parts

#### Part H
When \( i_3 \) has half of its final value, what is \( i_2 \)?

**Instructions:** 
- Express your answer with the appropriate units.
- Use the provided answer box to input the value and units for \( i_2 \).

\( i_2 = \text{Value} \, \text{Units} \)

#### Part I
When \( i_3 \) has half of its final value, what is \( i_1 \)?

**Instructions:** 
- Express your answer with the appropriate units.
- Use the provided answer box to input the value and units for \( i_1 \).

\( i_1 = \text{Value} \, \text{Units} \)

### Note
Analyze the circuit using Kirchhoff’s rules and the properties of inductors to solve for the unknown currents at the given conditions.
Transcribed Image Text:### Educational Content: Inductor Circuit Analysis An inductor with an inductance \( L = 0.400 \, \text{H} \) and negligible resistance is connected to a battery, a switch \( S \), and two resistors, \( R_1 = 11.0 \, \Omega \) and \( R_2 = 15.0 \, \Omega \), as shown in Figure 1. The battery has an electromotive force (emf) of 96.0 V and negligible internal resistance. The switch \( S \) is closed at time \( t = 0 \). #### Circuit Diagram (Figure 1) - The circuit consists of the following components: - A battery \( \mathcal{E} \) providing a voltage of 96.0 V. - A switch \( S \), initially open, is closed at time \( t = 0 \). - A resistor \( R_1 = 11.0 \, \Omega \) with current \( i_2 \) flowing through it. - A resistor \( R_2 = 15.0 \, \Omega \) in series with an inductor with current \( i_3 \) flowing through this branch. - An inductor \( L = 0.400 \, \text{H} \). - Three currents: \( i_1 \), \( i_2 \), and \( i_3 \). ### Problem Parts #### Part H When \( i_3 \) has half of its final value, what is \( i_2 \)? **Instructions:** - Express your answer with the appropriate units. - Use the provided answer box to input the value and units for \( i_2 \). \( i_2 = \text{Value} \, \text{Units} \) #### Part I When \( i_3 \) has half of its final value, what is \( i_1 \)? **Instructions:** - Express your answer with the appropriate units. - Use the provided answer box to input the value and units for \( i_1 \). \( i_1 = \text{Value} \, \text{Units} \) ### Note Analyze the circuit using Kirchhoff’s rules and the properties of inductors to solve for the unknown currents at the given conditions.
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