Question

When a capacitor, battery, and resistor are connected in series, does the resistor affect the maximum charge stored on the capacitor? Why or why not? What purpose does the resistor serve?

Short answer

Resistance does not affect the maximum charge on the capacitor.

A resistor will affect the time constant which gives us how quickly the capacitor charges.

Step-by-step solution

R-C Circuit

In RC circuit resistor with resistance R and capacitor with capacitance C are connected in the circuit wich has a energy source. The charging and discharging takes place in the RC circuit after we connect it to exeternal source.

Affect of Resistance on charge on the capactor    

The final charge of the capacitor is given by :

Q = CV

Here V is the voltage of the battery.

Since it does not depend on on-resistance, R does not affect the maximum charge on the capacitor. As it depends on its own capacitance and battry voltage only.

Affect of resistance on the time constant

The time for charge completion is given by:

τ = RC

A resistor will affect the time constant which gives us how quickly the capacitor charges. As it depends on the resistance R and capacitance of its own.