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Charging of the metal sphere through the current limiting resistor

QuickField simulation example

Simulate the charging process, determine the charging time, and calculate the maximum current.

Problem Type

Transient electric field

Geometry

Sphere is connected through a resistor to the source and to the ground metal sphere equivalent circuit
All dimensions are in mm Equivalent circuit

Given

Relative permittivity of the air ε = 1;
Conductivity of metal g = 8 000 000 S/m;
Resistor R = 0.8 Ohm;
Nominal voltage E = 1.5 V.

Solution

This system can be represented by an equivalent circuit with voltage source E, resistor R and capacitor C connected in series. The ground potential is zero. Resistor R limits the charging current value. Resistor is modeled directly in the QuickField problem by the block "resistor".

Results

First the current hits the maximum value of 3.5 A. Then the current decreases rapidly and at 3*10-10s. the process ends (99.9% of full charge).
metal sphere charging current
metal sphere electric field

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