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In the circuit below, the switch has been in the open position for a long time. At t=0, the switch is turned on. If the current at time t=1.1 ms reaches 75% of its maximum value, R=25 Ω, and ℰ=15 V, find: the maximum value of the current, Imax=  A. the time constant τ=  ms, the inductance L=  mH. If the switch is open again, after what time, the current will reach 25% of its value? t1/4=  ms.

In the circuit below, the switch has been in the open position for a long time. At t=0, the switch is turned on. If the current at time t=1.1 ms reaches 75% of its maximum value, R=25 Ω, and ℰ=15 V, find: the maximum value of the current, Imax=  A. the time constant τ=  ms, the inductance L=  mH. If the switch is open again, after what time, the current will reach 25% of its value? t1/4=  ms.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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In the circuit below, the switch has been in the open position for a long time. At t=0, the switch is turned on. If the current at time t=1.1 ms reaches 75% of its maximum value, R=25 Ω, and ℰ=15 V, find:

the maximum value of the current, Imax=  A.

the time constant τ=  ms,

the inductance L=  mH.

If the switch is open again, after what time, the current will reach 25% of its value?

t1/4=  ms.

### Description of an RL Circuit The image presents a diagram of a simple RL (Resistor-Inductor) circuit. Below is a detailed explanation of the components and connections in the circuit: 1. **Components:** - **Battery (ε):** It is represented by a symbol with a long and a short parallel line, indicating the positive (+) and negative (-) terminals, respectively. This component provides the electromotive force (EMF) to the circuit. - **Switch (S):** Indicated by the letter "S" with a representation of an open switch. This component controls the flow of current in the circuit. - **Inductor (L):** Represented by a series of coil loops. An inductor stores energy in its magnetic field when current passes through it. - **Resistor (R):** Denoted by a zigzag line and the letter "R". The resistor limits the current flow and dissipates energy as heat. 2. **Connections:** - The positive terminal of the battery is connected to one end of the switch. - The other end of the switch is connected to one end of the inductor (L). - The other end of the inductor is connected to one end of the resistor (R). - The other end of the resistor connects back to the negative terminal of the battery, thus completing the circuit. 3. **Operation:** - When the switch (S) is closed, it completes the circuit, allowing current to flow from the positive terminal of the battery, through the switch, into the inductor, through the resistor, and back to the negative terminal of the battery. - When the switch is open, the current flow is interrupted, and the circuit is incomplete. ### Educational Purpose This diagram is often used in educational settings to teach fundamental concepts of electrical circuits, particularly how inductors and resistors interact within a circuit. It demonstrates the following principles: - **Ohm's Law:** Relationship between voltage (V), current (I), and resistance (R): \( V = IR \). - **Inductance:** How inductors oppose changes in current. - **Transient Response:** Understanding how the current and voltage change over time when the switch is opened or closed. - **Energy Storage:** Inductors store energy in a magnetic field, and resistors dissipate energy as heat. Understanding this RL circuit is foundational for students learning about more complex electrical
Transcribed Image Text:### Description of an RL Circuit The image presents a diagram of a simple RL (Resistor-Inductor) circuit. Below is a detailed explanation of the components and connections in the circuit: 1. **Components:** - **Battery (ε):** It is represented by a symbol with a long and a short parallel line, indicating the positive (+) and negative (-) terminals, respectively. This component provides the electromotive force (EMF) to the circuit. - **Switch (S):** Indicated by the letter "S" with a representation of an open switch. This component controls the flow of current in the circuit. - **Inductor (L):** Represented by a series of coil loops. An inductor stores energy in its magnetic field when current passes through it. - **Resistor (R):** Denoted by a zigzag line and the letter "R". The resistor limits the current flow and dissipates energy as heat. 2. **Connections:** - The positive terminal of the battery is connected to one end of the switch. - The other end of the switch is connected to one end of the inductor (L). - The other end of the inductor is connected to one end of the resistor (R). - The other end of the resistor connects back to the negative terminal of the battery, thus completing the circuit. 3. **Operation:** - When the switch (S) is closed, it completes the circuit, allowing current to flow from the positive terminal of the battery, through the switch, into the inductor, through the resistor, and back to the negative terminal of the battery. - When the switch is open, the current flow is interrupted, and the circuit is incomplete. ### Educational Purpose This diagram is often used in educational settings to teach fundamental concepts of electrical circuits, particularly how inductors and resistors interact within a circuit. It demonstrates the following principles: - **Ohm's Law:** Relationship between voltage (V), current (I), and resistance (R): \( V = IR \). - **Inductance:** How inductors oppose changes in current. - **Transient Response:** Understanding how the current and voltage change over time when the switch is opened or closed. - **Energy Storage:** Inductors store energy in a magnetic field, and resistors dissipate energy as heat. Understanding this RL circuit is foundational for students learning about more complex electrical
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