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### Inductive Circuit Analysis **Introduction:** An inductor with 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 \( R_2 = 15.0 \, \Omega \). The battery has an electromotive force (emf) of \( 96.0 \, \text{V} \) with negligible internal resistance. The switch \( S \) is closed at \( t = 0 \). **Figure Explanation:** The given circuit diagram depicts: - A battery with emf \( \mathcal{E} = 96.0 \, \text{V} \). - A switch \( S \) in series with resistor \( R_1 \). - Current \( i_1 \) flows through the circuit including the battery and switch. - Resistor \( R_1 \) with current \( i_2 \) flowing downwards. - Resistor \( R_2 \) in series with an inductor \( L \). - Current \( i_3 \) flows through resistor \( R_2 \) and the inductor. **Problem Statements:** **Part E:** - What is the current \( i_3 \) after \( S \) has been closed a long time? - Express your answer with the appropriate units. **Part F:** - What is the current \( i_1 \) after \( S \) has been closed a long time? - Express your answer with the appropriate units. In both parts, provide the current values and units. This problem explores the behavior of the circuit as it reaches a steady state over a considerable duration with the switch closed.
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Transcribed Image Text:### Inductive Circuit Analysis **Introduction:** An inductor with 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 \( R_2 = 15.0 \, \Omega \). The battery has an electromotive force (emf) of \( 96.0 \, \text{V} \) with negligible internal resistance. The switch \( S \) is closed at \( t = 0 \). **Figure Explanation:** The given circuit diagram depicts: - A battery with emf \( \mathcal{E} = 96.0 \, \text{V} \). - A switch \( S \) in series with resistor \( R_1 \). - Current \( i_1 \) flows through the circuit including the battery and switch. - Resistor \( R_1 \) with current \( i_2 \) flowing downwards. - Resistor \( R_2 \) in series with an inductor \( L \). - Current \( i_3 \) flows through resistor \( R_2 \) and the inductor. **Problem Statements:** **Part E:** - What is the current \( i_3 \) after \( S \) has been closed a long time? - Express your answer with the appropriate units. **Part F:** - What is the current \( i_1 \) after \( S \) has been closed a long time? - Express your answer with the appropriate units. In both parts, provide the current values and units. This problem explores the behavior of the circuit as it reaches a steady state over a considerable duration with the switch closed.
**Part G** What is the value of \( t \) for which \( i_3 \) has half of the final value that you calculated in part E? *Express your answer with the appropriate units.* - Input box for \( t = \) with fields for "Value" and "Units". **Part H** When \( i_3 \) has half of its final value, what is \( i_2 \)? *Express your answer with the appropriate units.* - Input box for \( i_2 = \) with fields for "Value" and "Units".
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Transcribed Image Text:**Part G** What is the value of \( t \) for which \( i_3 \) has half of the final value that you calculated in part E? *Express your answer with the appropriate units.* - Input box for \( t = \) with fields for "Value" and "Units". **Part H** When \( i_3 \) has half of its final value, what is \( i_2 \)? *Express your answer with the appropriate units.* - Input box for \( i_2 = \) with fields for "Value" and "Units".
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