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A circuit contains a capacitor and inductance each with negligible resistance. The capacitor is initially charged and the charging battery is disconnected. At subsequent time, the charge on the capacitor will A) decrease linearly B)decrease exponentially C)remain constant?
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A circuit contains a capacitor and inductance each with negligible res...
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A circuit contains a capacitor and inductance each with negligible res...
Introduction:
In this circuit, we have a capacitor and an inductance connected in series with negligible resistance. The capacitor is initially charged, and the charging battery is disconnected. We need to determine how the charge on the capacitor will change over time.

Explanation:
When the charging battery is disconnected, the capacitor and inductor form a closed circuit. The capacitor stores energy in the form of electric field, while the inductor stores energy in the form of a magnetic field.

1. Energy Transfer:
Initially, the capacitor is fully charged, and it holds a certain amount of energy. As the circuit is closed, the capacitor starts discharging, and its energy is transferred to the inductor. The electric field across the capacitor decreases, and the magnetic field in the inductor increases.

2. Inductor Behavior:
According to Faraday's law of electromagnetic induction, a changing magnetic field induces an electromotive force (emf) in the inductor. This emf opposes the change in current through the inductor. As a result, the inductor resists any change in current and acts as a source of energy.

3. Charging and Discharging Currents:
Initially, when the capacitor starts discharging, the current flows through the inductor and decreases over time. This decreasing current induces a back emf in the inductor, which opposes the current's decrease. Consequently, the charge on the capacitor decreases exponentially rather than linearly.

4. Exponential Decay:
The rate of change of charge on the capacitor is proportional to the current flowing through the inductor. Since the current decreases exponentially, the rate of change of charge on the capacitor also decreases exponentially. This leads to an exponential decay in the charge on the capacitor over time.

Conclusion:
Therefore, the charge on the capacitor will decrease exponentially over time when the charging battery is disconnected in a circuit containing a capacitor and inductance with negligible resistance.
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Read the following text and answer the following questions on the basis of the same: TOROIDA toroid is a coil of insulated or enamelled wire wound on a donut-shaped form made of powdered iron. A toroid is used as an inductor in electronic circuits, especially at low frequencies where comparatively large inductances are necessary. A toroid has more inductance , for a given number of turns, than a solenoid with a core of the same material and similar size. This makes it possible to construct high-inductance coils of reasonable physical size and mass. Toroidal coils of a given inductance can carry more current than solenoidal coils of similar size, because larger-diameter wires can be used, and the total amount of wire is less, reducing the resistance . In a toroid, all the magnetic flux is contained in the core material. This is because the core has no ends from which flux might leak off. The confinement of the flux prevents external magnetic fields from affecting the behaviour of the toroid, and also prevents the magnetic field in the toroid from affecting other components in a circuit. Standard toroidal transformers typically offer a 95% efficiency, while standard laminated transformers typically offer less than a 90% rating. One of the most important differences between a toroidal transformer and a traditional laminated transformer is the absence of gaps. The leakage flux through the gaps contributes to the stray losses in the form of eddy currents (which is also expelled in the form of heat). A toroidal core doesn’t have an air gap. The core is tightly wound . The result is a stable, predictable toroidal core, free from discontinuities and holes. Audible vibration or hum in transformers is caused by vibration of the windings and core layers from the forces between the coil turns and core laminations. The toroidal transformer’s construction helps quiet this noise. In audio, or signal transmitting applications, unwarranted noise will affect sound quality, so a transformer with low audible vibration is ideal. For this reason, many sound system engineers prefer to use a toroidal transformer instead of a traditional laminated transformer.Why inductance of solenoid is more than the inductance of a solenoid having same number of turns, core of same material and similar size?

Read the following text and answer the following questions on the basis of the same:TOROIDA toroid is a coil of insulated or enamelled wire wound on a donut-shaped form made of powdered iron. A toroid is used as an inductor in electronic circuits, especially at low frequencies where comparatively large inductances are necessary. A toroid has more inductance , for a given number of turns, than a solenoid with a core of the same material and similar size. This makes it possible to construct high-inductance coils of reasonable physical size and mass. Toroidal coils of a given inductance can carry more current than solenoidal coils of similar size, because larger-diameter wires can be used, and the total amount of wire is less, reducing the resistance . In a toroid, all the magnetic flux is contained in the core material. This is because the core has no ends from which flux might leak off. The confinement of the flux prevents external magnetic fields from affecting the behaviour of the toroid, and also prevents the magnetic field in the toroid from affecting other components in a circuit. Standard toroidal transformers typically offer a 95% efficiency, while standard laminated transformers typically offer less than a 90% rating. One of the most important differences between a toroidal transformer and a traditional laminated transformer is the absence of gaps. The leakage flux through the gaps contributes to the stray losses in the form of eddy currents (which is also expelled in the form of heat). A toroidal core doesn’t have an air gap. The core is tightly wound . The result is a stable, predictable toroidal core, free from discontinuities and holes. Audible vibration or hum in transformers is caused by vibration of the windings and core layers from the forces between the coil turns and core laminations. The toroidal transformer’s construction helps quiet this noise. In audio, or signal transmitting applications, unwarranted noise will affect sound quality, so a transformer with low audible vibration is ideal. For this reason, many sound system engineers prefer to use a toroidal transformer instead of a traditional laminated transformer.A toroid has _____ inductance, for a given number of turns, than a solenoid with a core of the same material and similar size.

A circuit contains a capacitor and inductance each with negligible resistance. The capacitor is initially charged and the charging battery is disconnected. At subsequent time, the charge on the capacitor will A) decrease linearly B)decrease exponentially C)remain constant?
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A circuit contains a capacitor and inductance each with negligible resistance. The capacitor is initially charged and the charging battery is disconnected. At subsequent time, the charge on the capacitor will A) decrease linearly B)decrease exponentially C)remain constant? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A circuit contains a capacitor and inductance each with negligible resistance. The capacitor is initially charged and the charging battery is disconnected. At subsequent time, the charge on the capacitor will A) decrease linearly B)decrease exponentially C)remain constant? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circuit contains a capacitor and inductance each with negligible resistance. The capacitor is initially charged and the charging battery is disconnected. At subsequent time, the charge on the capacitor will A) decrease linearly B)decrease exponentially C)remain constant?.
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