Determine the range of possible values for VC for the network of Fig. 132 using the 1-M Ωpotenti

step 1 This problem is going to deal with a delta Y transformation. It's also going to use OMS law, of

Determine the range of possible values for VC for the...

Key Concepts

Potentiometer

A potentiometer is a three-terminal variable resistor that acts as an adjustable voltage divider. By moving its wiper along a resistive element, the ratio of the resistances on either side of the wiper changes, thereby modifying the voltage output. This principle is widely used to control and fine-tune voltage levels within circuits.

Voltage Divider

The voltage divider is a fundamental circuit configuration where two or more resistors are connected in series and the input voltage is proportionally divided among them. It is governed by the ratio of the resistors, making it a crucial concept in determining how voltage is shared across different parts of a circuit.

Extreme Value Analysis in Circuits

Extreme value analysis in circuits involves evaluating the behavior of circuit outputs under boundary conditions, such as the maximum and minimum settings of a variable component like a potentiometer. This approach is essential for understanding the limits and operational range of circuit parameters, ensuring the design meets performance and safety criteria.

Transcript

00:01 This problem is going to deal with a delta y transformation.

00:05 It's also going to use oms law, of course, and it's going to use the formula that we have for total resistance, either in a series or in a parallel circuit.

00:16 I've redrawn the circuit so that it's a little more clear where the y is going to be.

00:25 So we're going to turn that into a delta.

00:29 And then we'll transform that into a y.

00:33 And eventually we're going to work our way down so that we find v0, the voltage drop across that 6 kilo -oam resistor.

00:43 So for a delta y transformation, what we'll do is over here, i'll go ahead and put in these values for these resistances.

00:55 So i have 6 kilo -ooms.

00:58 I have 18 kilo -ooms and i have 12 kilooms.

01:05 And for each of these corners, a, b, and c, then we have an equivalent resistance over here.

01:13 And to find that resistance, we multiply the two resistors on either side of that corner and then divide by the total of the resistances.

01:23 So for instance, for let's say resistance c, which will be over here at this leg, resistance c is going to be equal to 6, which is r1, times 12, which is r3, and that will be kilo -ooms.

01:43 And that's going to be divided by the sum of the resistances, that's kilowatoms squared, some of the resistances which is 36 kilo -ooms and so resistance c is going to be equal to two kilo -ooms and so we'll do that for the other ones and then we can draw the circuit with a y branch so that two kilo -ooms is over here for our b that is 18 times 12 divided by 36, it gives me 6 kilo -ooms, and then here was 6 times 18 divided by 36, that gives me 3 kilo -ooms, and i have 4 and 6 down here.

02:30 And so for this branch here, my total resistance will be 12 kilo -ooms, and here i'll have 6 kilo -ooms, and then i can combine those because their resistance for parallel is going to be 1 over, 1 over 6 plus 1 over 12.

02:48 And so the resistance of that part of the branch is going to be four kilo -ooms...

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