Question

A low-pass$RC$ filter with a crossover frequency of $1000Hz$uses a $100\Omega$resistor. What is the value of the capacitor?

Short answer

Value of the capacitor,$C=1.59\mu \mathrm{F}$

Step-by-step solution

Capacitor

A capacitor may be a device for storing power that consists of two insulated conductors in close proximity.

The parallel-plate capacitor may be a simple example of such a storage device.

Find the capacitor

$f=1000\mathrm{Hz}$(hertz)

$R=100\Omega$(ohm)

The frequency of crossover is

$w=\frac{1}{RC}$

$2\pi f=\frac{1}{RC}$

$R$multiply each sides of the equation.

$2\pi fR=\frac{1}{C}$

$C=\frac{1}{2\pi fR}$

Substitute the values

localid="1650212157053" $C=\frac{1}{2\pi \times \left(1000\right)Hz\times \left(100\right)\Omega }$

$C=1.59\mu \mathrm{F}$(micro frequency)