Question

Question: How does the final (equilibrium) charge on the capacitor plates depend on the particular resistor (for example, the kind of bulb or the length of Nichrome wire) in the circuit during charging? Explain briefly.

Short answer

The capacitor's charging depends on the cross-sectional area of the wire or filament of the bulb.

Step-by-step solution

Assume some data on behalf of given question.

Let assume the resistance of the filament of the nichrome wire is$R$ .

Area of the capacitor plates is $A$.

Determine the formulas that shows the relation between the final charge and resistance of the element.

The electron charge or current is defined as the number of the electron enter the wire every second.

The expression to calculate the electron current at the location $D$is given as follows.

role="math" localid="1668592073069" $i=nA\mu E$ …… (i)

Here, is the number of the electron, is the cross-sectional area, is the mobility and is the electrical field.

Determine that how the final charge on the capacitor depends on the particular resistance.

The electric field inside the capacitor plates is constant, and the current in the filament of the bulb and wire varies during the charging. The mobility is a constant value for the particular material. Therefore, the current depends on the cross-sectional area.

From equation (i), the current in the bulb's filament is directly proportional to the cross-sectional area. If the cross-sectional area of the wire or filament of the bulb is low, then the current through the wire and bulb's filament is low.

Hence, the capacitor's charging depends on the cross-sectional area of the wire or filament of the bulb.