# Capacitor and Variable resistor

• coldturkey
In summary: The way I did it:I = q/tq = CVso I = CV/tand R = V/Iand solved it for all 4 cases:(max voltage, largest discharge time)(max voltage, smallest discharge time)(min voltage, largest discharge time)(min voltage, smallest discharge time)(24.8 ohms, 14882 ohms)
coldturkey
A controller on an electronic arcade game consists of a variable resistor connected across the plates of a $$0.220\mu F$$ capacitor. The capacitor is charged to $$5.00V$$, then discharged through the resistor. The time for the potential difference across the plates to decrease to $$0.800V$$ is measured by a clock inside the game. If the range of discharge times that can be handled effectivly is from $$10.0\mu s$$ to $$6.00ms$$, what should be the resistance range of the resistor?

I have solved the problem and I get a maximum resistance of $$27272.7\Omega$$ and a minimum resistance of $$45.45\Omega$$.
But these values seem a bit too large.

The way I did it:
$$I = q/t$$
$$q = CV$$
so $$I = CV/t$$
and $$R = V/I$$

and solved it for all 4 cases:
(max voltage, largest discharge time)
(max voltage, smallest discharge time)
(min voltage, largest discharge time)
(min voltage, smallest discharge time)

An found there are two different values for the resistor:
$$27272.7\Omega$$ and $$45.45\Omega$$.

Does anyone know if there is anything I have done wrong?
Many thanks

I think you can use the formula:
$$V=V_{0}e^{-\frac{t}{RC}}$$

I tried it using your formula and I get 24.8 ohms and 14882 ohms.
This is roughly half of what I got before.
Any ideas?

the way it is worded, cartoon kid is correct.

jw, but what was your reasoning behind this?

coldturkey said:
and solved it for all 4 cases:
(max voltage, largest discharge time)
(max voltage, smallest discharge time)
(min voltage, largest discharge time)
(min voltage, smallest discharge time)

Last edited:
coldturkey said:
I tried it using your formula and I get 24.8 ohms and 14882 ohms.
This is roughly half of what I got before.
Any ideas?

In a RC circuit, when a capacitor is discharging, the charges, current and voltage across the capacitor are decreasing exponentially. It's a continuous process. The bigger the R, the slower the discharing process.

well I wasnt sure what the relationships were all about so I just decided to try all possible cases and see what I came up with.

## What is a capacitor?

A capacitor is an electronic component that stores electrical charge. It is made of two conductive plates separated by an insulating material, also known as a dielectric. When a voltage is applied, electrons accumulate on one plate while an equal number of electrons are removed from the other plate, creating an electric field between them.

## What is the purpose of a capacitor?

Capacitors are used in electronic circuits for a variety of purposes, including filtering and smoothing out AC signals, storing energy, and blocking DC signals from entering certain parts of the circuit.

## How does a variable resistor work?

A variable resistor, also known as a potentiometer, is a resistor with a third terminal that can be adjusted to change the resistance. This is achieved by moving a wiper along a resistive element, changing the length of the resistive path and therefore the amount of resistance. This allows for precise control of the current or voltage in a circuit.

## What are some applications of a capacitor?

Capacitors are used in a wide range of electronic devices and systems, including power supplies, audio amplifiers, radios, televisions, computers, and many more. They are also commonly used in motor starting circuits, timing circuits, and in electronic filters for signal processing.

## Can a capacitor and variable resistor be used together?

Yes, capacitors and variable resistors are often used together in electronic circuits. For example, a capacitor and variable resistor can be used in an RC circuit to control the frequency of a signal. Additionally, variable resistors can be used to adjust the charging and discharging rates of a capacitor, allowing for precise control of the time constant in a circuit.

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