**Circuit Analysis with Inductance and Capacitance**In the circuit of the figure below, the battery emf \( \mathcal{E} \) is 55 V, the resistance \( R \) is 210 \( \Omega \), and the capacitance \( C \) is 0.500 \( \mu F \). The switch \( S \) is closed for a long time interval, and zero potential difference is measured across the capacitor. After the switch is opened, the potential difference across the capacitor reaches a maximum value of 150 V. What is the value of the inductance?**Diagram Explanation:**- **Diagram Components:** - Battery with emf \( \mathcal{E} \) connected in series. - Resistor \( R \) connected next to the battery. - Inductor \( L \) and capacitor \( C \) connected in parallel. - Switch \( S \) positioned before the capacitor-inductor series.**Circuit Description:**The circuit consists of a battery providing an electromotive force (emf), a resistor, an inductor, a capacitor, and a switch. Initially, the circuit is closed for a significant period indicating a steady-state where the capacitor is fully charged and potential difference is zero. When the switch is opened, the circuit allows the voltage across the capacitor to reach a maximum value due to the inductor’s energy release. This scenario is typical of an LC circuit where energy oscillates between the capacitor and inductor.The task is to determine the inductance \( L \) using these circuit conditions.

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time intérval, and zero potential difference is measured across the capacitor. After the switch is dpened, the potential difference reaches a maximum value of 150 V. What is the value of the inductance? R L. S

time intérval, and zero potential difference is measured across the capacitor. After the switch is dpened, the potential difference reaches a maximum value of 150 V. What is the value of the inductance? R L. S

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Voltage Across Inductor

An actor is a passive electrical component that consists of a coil bent in the form of wire which uses electromagnetism to produce electric current through the coil. When the electric current flows through a conductor that is the coil, a magnetic flux is developed around the conductor. This flow of current through the coil creates a magnetic field based on Fleming's Right-hand thumb rule. If there is any decrease in the current passing through the inductor, then the magnetic field will also decrease and energy is released through the generation of electric current. There is also a secondary voltage inducing in the same coil due to the magnetic flux, since it opposes any changes in the electric current flowing through the circuit. An inductor is also called choke, coil, or solenoid. A choke is designed to block certain frequencies when the DC current passes. A winding coil is coated with insulation to give extra insulation and protect the circuit. They are usually tightly wrapped around a central core which is cylindrical in nature so that the magnetic flux can be induced. The solenoid is a three-dimension coil that is used to exhibit electromagnetism when the magnetic field is developed due to the current flowing through the coil. The sign convention of the inductor is the same as the power dissipating device. When the current flows into the positive side of the voltage across the inductor, the value is positive and the inductor dissipates power whereas when the inductor releases the power back to the circuit, the current has a negative sign convention. 

Question

**Circuit Analysis with Inductance and Capacitance**

In the circuit of the figure below, the battery emf \( \mathcal{E} \) is 55 V, the resistance \( R \) is 210 \( \Omega \), and the capacitance \( C \) is 0.500 \( \mu F \). The switch \( S \) is closed for a long time interval, and zero potential difference is measured across the capacitor. After the switch is opened, the potential difference across the capacitor reaches a maximum value of 150 V. What is the value of the inductance?

**Diagram Explanation:**

- **Diagram Components:**
- Battery with emf \( \mathcal{E} \) connected in series.
- Resistor \( R \) connected next to the battery.
- Inductor \( L \) and capacitor \( C \) connected in parallel.
- Switch \( S \) positioned before the capacitor-inductor series.

**Circuit Description:**

The circuit consists of a battery providing an electromotive force (emf), a resistor, an inductor, a capacitor, and a switch. Initially, the circuit is closed for a significant period indicating a steady-state where the capacitor is fully charged and potential difference is zero. When the switch is opened, the circuit allows the voltage across the capacitor to reach a maximum value due to the inductor’s energy release. This scenario is typical of an LC circuit where energy oscillates between the capacitor and inductor.

The task is to determine the inductance \( L \) using these circuit conditions.

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