Introductory lvl circuit analysis problem

[t3rom]

Homework Statement

Your factory is building RC low-pass filters using 10-6 F capacitors and 1k Ohm resistors. Suddenly the worldwide supply of capacitors dries up and you now have to build filters with the same electrical characteristics but you have to use inductors and resistors rather than capacitors and resistors. If you want to continue using your supply of 1k Ohm resistors, what value inductors should you use to build low-pass filters with the same characteristics as the RC filters you were building?

Homework Equations

None

The Attempt at a Solution

I'm looking for an equation to solve this problem but I've none in my notes. The answer is in Henry (i.e. we are looking for inductor value). Can someone kindly help me understand and solve this problem? TIA!

 

[The Electrician]

Have a look at these two pages:

http://en.wikipedia.org/wiki/RC_circuit

http://en.wikipedia.org/wiki/RL_circuit

Note that the RL circuit is not a low pass; you will have to make an appropriate change.

 

[t3rom]

I did have those RC and RL equations in my notes, but I don't understand how to get the value of L from C and R. The answer is 1H btw.

 

[The Electrician]

Figure out what the corner frequency is for the R-C low pass. Analyze the L-R low pass; it will have to use the same value of R. Figure out what value of L will give the same corner frequency.

 

[rezeew]

I would approach this problem by first understanding the characteristics of a low-pass filter. A low-pass filter is a circuit that allows low frequency signals to pass through while blocking high frequency signals. This is achieved by using a combination of a resistor and a capacitor. In this case, we are using a 10-6 F capacitor and a 1k Ohm resistor.

Now, if we have to use inductors instead of capacitors, we need to understand how an inductor works. An inductor is a passive component that stores energy in the form of a magnetic field. It resists changes in current flow and has the ability to pass high frequency signals while blocking low frequency signals.

To solve this problem, we can use the concept of impedance. Impedance is the total opposition to the flow of current in an alternating current circuit. In a low-pass filter, the impedance at low frequencies is dominated by the resistor, while at high frequencies it is dominated by the capacitor.

Since we want to maintain the same characteristics of the filter, we need to find an inductor that will have the same impedance as the capacitor at high frequencies. This can be achieved by using the equation Z = √(R^2 + XL^2), where Z is the impedance, R is the resistance, and XL is the inductive reactance.

We know that the value of R is 1k Ohm, and we want to find the value of XL that will give us the same impedance as the 10-6 F capacitor. Using the equation, we can rearrange it to solve for XL, which gives us XL = √(Z^2 - R^2). Plugging in the values, we get XL = √(1k^2 - 10^-12) = 999 Ohms.

Therefore, to build low-pass filters with the same characteristics as the RC filters, we need to use inductors with a value of 999 Ohms. This will ensure that the impedance at high frequencies is the same as the 10-6 F capacitor, allowing the low-pass filter to function in the same way.