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In normal battery resistor circuits, battery doesn't store any charge, its basically the free electrons of resistors /conducting wire that moves in a circuit. But in discharging of capacitor, charge stored on the capacitor moves. Do free electrons of the wires move too?

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In normal battery resistor circuits, battery doesn't store any charge,

A battery does not "store" charge in the sense that it does not supply charge to the circuit. The battery separates charge at its terminals creating a potential difference between the positive and negative terminals. So a battery stores electrical potential energy from the conversion of stored chemical potential energy.

it's basically the free electrons of resistors /conducting wire that moves in a circuit.

Correct. But they get their energy to do so from the electrical potential energy of the battery and, ultimately, from the stored chemical potential energy of the battery.

But in discharging of capacitor, charge stored on the capacitor moves

Correct. When the capacitor discharges, electrons come off the negatively charged plate of the capacitor and an equal number of electrons are supplied to the positively charged plate eventually neutralizing that plate. This movement of charge constitutes the capacitor current.

Do free electrons of the wires move too?

Yes. You can think of the capacitor as being a small (relatively low energy) battery that only stores electrical potential energy (no chemical potential energy).

During discharge, the positively charged plate of the capacitor attracts free electrons from the wires while the negatively charged plate supplies free electrons to the wires. But since, unlike the battery, there is no stored chemical potential energy to replenish the electrical potential energy lost by the capacitor in moving the electrons, the positive and negative plates are eventually neutralized with no electrical potential energy remaining. At this point the current stops.

Hope this helps.

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In normal battery resistor circuits ,battery doesn't store any charge

Yes the battery has charge. Charge is necessary for there to be voltage at the terminals. Batteries replenish their charges through chemical action, but it is wrong to say there is no stored charge present. It plays an essential role in causing current to flow.

its basically the free electrons of resistors /conducting wire that moves in a circuit .

Charges move somewhat slowly in a circuit. But when charges move down a wire away from the battery, charges in the battery terminal move into the wire. Similarly for other components in a circuit.

But in discharging of capacitor ,charge stored on the capacitor moves .

Yes, it moves into the wire

Does free electrons of the wires move too ?

Yes, electrons in the wire move to.

In general, electrons move throughout a circuit that has current in it (except across the dielectric in a capacitor, where there is displacement current rather than conduction current.)

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