Question

How do resistors affect capacitors?

Answer 1

In this question, we will use the two basic formulas, one is the Ohm’s law and the second one is the relation between capacitance, charge and the voltage. Further, by using the basic definitions we will answer the given question step by step. Also, we will study the basics of a simple circuit.

Formula used:
$I = V \times R$
$V = \dfrac{Q}{C}$

Complete solution:
As we know that when capacitors and resistors both are connected together, then the resistor resists the flow of current that can charge or discharge the connected capacitor.
Now, we know that the larger the value of the resistor, the slower the charge or discharge rate.

Also, we know the larger the value of a capacitor, the slower the charge or discharge rate.
Further, when we apply a voltage to a capacitor through a resistor which is connected in series, then the current will be highest when the capacitor has zero volts flowing in it.

As we know that the maximum charge current is limited to:
Here, I is the current, V is the applied voltage and R is the series resistance, connected to the circuit.

Now, in the circuit the voltage on the connected capacitor changes when this given capacitor charges or discharges.

So, when this capacitor gets charged, then the voltage flowing across the resistor drops, which can be given by:
${V_R} = V - {V_{cap}}$
So, as the voltage drops then the current flowing through it also drops.

This gives us a charge curve that starts off when it reaches its maximum charge rate and it tails off to a slower and slower charge rate as the capacitor reaches its fully charged state.

${V_b} = {V_R} + {V_C}$
$\Rightarrow {V_b} = IR + \dfrac{Q}{C}$

Now, in the above equation we can see that when Q charge increases, current I decrease.

Additional information:
We should know that in a series circuit, the output current of the first resistor flows into the input of the second resistor; so, the current is the same in each resistor whereas In a parallel circuit, all of the resistor are on connected together on one side and all the leads on the other side are connected together.

In a circuit if the resistance is constant over a range of voltage, then I = V/R, can be used to predict the behavior of the material. This involves DC current and voltage, it is the same for the resistors.

Note:
In series connection the resistances are directly added whereas in parallel connection resistance is added inversely. Internal resistance of a circuit refers to the opposition to the flow of current offered by the cells and batteries themselves thereby, resulting in the generation of heat.