# Series LC Circuit: Charging Capacitor & Current Flow w/ 0V Inductor

• likephysics
In summary, the capacitor is charged by a switch to the battery voltage. When the switch is closed, the capacitor starts discharging through the inductor. The capacitor is charged to 2V, but this is not always the case.

#### likephysics

In a series LC ckt, the capacitor charges to the applied voltage V after some time t1secs. Now there is no voltage across the inductor.
How can the inductor keep supplying current to the capacitor, when the potential difference across it is zero.
The capacitor is charged up to 2V. Why just 2V?

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I feel like I'm missing information. What's "2V" referring to? Is there a power source in this circuit? Do we charge the capacitor, then add it to the circuit after it's charged?

Well I have 2 cases:
1.
Just an LC circuit connected to a voltage source thru a switch.
switch is closed and capacitor is charged to supply voltage V.
Now the switch is opened, the inductor opposes this change and an emf is developed across it
which is equal to - L. di/dt
This will continue charging the capacitor in the -ve direction. Why does the capacitor get charged to 2 times V.

2. Just an LC ckt with a switch (no voltage source) with the capacitor charged to V volts. When the switch is closed, the capacitor starts discharging thru the inductor. When the cap current reaches zero, the inductor begins charging the cap. The capacitor is charged up to 2V.
why 2V. why not more. conservation of energy?

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In the first case, the capacitor is charged to the battery voltage V, and then the battery is disconnected. The inductor current and inductor voltage is initially zero. The capacitor is switched to the inductor. The capacitor discharges through the inductor, and when the capacitor voltage is zero, the inductor current is maximum (down direction). The inductor then begins discharging its stored energy into the capacitor. Eventually, half a cycle later, the capacitor is fully charged to -V (note sign), and the inductor current is again zero (no stored energy). The capacitor is never charged to 2 times V. It oscillates between +V and -V. Because there is no resistor in the LC circuit, the stored energy is constant.
E = (1/2)C V2 + (1/2)L I2 = constant.
The equation for the inductor is
Vcapacitor = L dI/dt. (positive current flows down through inductor)
Whenever the capacitor has a positive voltage, the current through the inductor is increasing (dI/dt>0), and whenever the voltage across the capacitor is negative, the current through the inductor is decreasing (dI/dt<0).

## What is a Series LC Circuit?

A series LC circuit consists of a capacitor and an inductor connected in series. It is a type of electrical circuit that is used to store and transfer energy between the capacitor and the inductor through oscillations.

## How does a Series LC Circuit charge a capacitor?

When the circuit is first connected to a voltage source, the capacitor begins to charge. This causes the current to flow through the inductor, building up a magnetic field. As the current continues to flow, the magnetic field collapses and induces a voltage across the capacitor, causing it to charge even more. This process continues until the capacitor is fully charged.

## What is the role of the inductor in a Series LC Circuit?

The inductor acts as a source of energy storage in a series LC circuit. It stores energy in the form of a magnetic field and releases it back into the circuit when needed. It also helps to regulate the flow of current in the circuit.

## What happens to the current flow in a Series LC Circuit when the inductor has 0V?

When the inductor has 0V, the current flow in the circuit will be at its maximum. This is because, without a voltage across the inductor, there is no opposition to the flow of current. As a result, the capacitor will charge quickly and the current will reach its maximum value.

## How does the voltage across the capacitor change over time in a Series LC Circuit?

Initially, the voltage across the capacitor will be 0V as it is uncharged. As the capacitor charges, the voltage across it will increase, reaching its maximum when the capacitor is fully charged. The voltage will then decrease as the capacitor discharges, and the cycle will repeat as long as the circuit is connected to a voltage source.