You are working on an electronics project requiring a...

You are working on an electronics project requiring a variety of capacitors, but have only a large supply of 100 nF capacitors available. Show how you can connect these capacitors to produce each of the following equivalent capacitances: (a) $50 \mathrm{nF},$ (b) $450 \mathrm{nF},(\mathrm{c}) 25 \mathrm{nF},$ (d) 75 $\mathrm{nF.}$

Key Concepts

Capacitance

Capacitance is the measure of a capacitor's ability to store electrical charge and energy. It plays a crucial role in circuits for filtering, timing, and energy storage, and is measured in farads (F), with typical practical values in the range of nanofarads (nF) or microfarads (µF).

Parallel Combination

In a parallel combination, capacitors are connected such that their corresponding terminals are joined together, thereby directly adding their capacitances. The total or equivalent capacitance is given by the sum of the individual capacitances (C_total = C1 + C2 + ...). This configuration is commonly used when a larger capacitance than what is available from a single capacitor is required.

Series Combination

When capacitors are connected in series, the charge on each capacitor is the same, but the voltage divides among them. The equivalent capacitance in a series configuration is found using the formula: 1/C_total = 1/C1 + 1/C2 + ... . This results in an overall capacitance that is smaller than any individual capacitor in the network, making it a useful technique to effectively decrease the available capacitance value.

Transcript

00:01 So in this question, you have a lot of 100 nanofarant capacitors, and you want to connect them so that you will be able to find 50, 450 nanofarant, 25 nanofarant, and 75 nanofarret.

00:22 So just firstly by quickly observing it, you can see that.

00:27 Great.

00:28 Everything seems to be in the depths of 25.

00:31 So that is easy because we know that if we have a hundred nanofaran and we connect two of them in parallel, we will get, and we connect you of them in series, we will get 50, and then if we connect four of them in parallel, we will get 25.

00:50 So that's like the building blocks for all of these.

00:54 So let's first do a quick review of the loss of capacitors.

00:59 So in general, capacitors have some, it works the other way compared to resistors.

01:06 So in resistors, we know if everything's in series, you add them up, and if everything's in parallel, then you add the inverse of the resistance up.

01:16 But the capacitors is different.

01:18 In capacitance, if you have everything in parallel, since the total capacitance, it's the inverse that adds up.

01:31 But if you have everything in parallel, so if you have everything in series, it's the inverse that adds up, but if you have everything in parallel, it's going to say i actually just add up.

01:49 And the reason why it works this way is because the capacitance can be defined as epsilon a over d...

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