In simplest way to prove this formular RX=(R2/R1)R3?

To prove the formula RX = (R2/R1)R3, we can use the concept of parallel resistors in a circuit.

When resistors are connected in parallel, the total resistance is given by the formula:

1/RX = 1/R1 + 1/R2 + 1/R3

Rearranging this formula, we get:

RX = 1 / (1/R1 + 1/R2 + 1/R3)

Multiplying the numerator and denominator by R1*R2*R3, we get:

RX = R1*R2*R3 / (R2*R3 + R1*R3 + R1*R2)

Now, we can simplify this expression by factoring out R3 from the denominator:

RX = R1*R2*R3 / R3(R2 + R1 + R2)

Simplifying further, we get:

RX = R1*R2 / (R2 + R1)

Therefore, RX = (R2/R1)R3 as required.

Step 1: Define the variables

- R1: Resistance in parallel with R2
- R2: Resistance in series with R3
- R3: Resistance in parallel with R

Step 2: Use the formula for parallel resistors

The resistance of two resistors in parallel (R1 and R2) is given by:

```
1/R = 1/R1 + 1/R2
```

Step 3: Substitute into the formula for series resistors

The resistance of two resistors in series (R2 and R3) is given by:

```
R = R2 + R3
```

Step 4: Combine the formulas

Substituting the parallel resistor formula into the series resistor formula, we get:

```
R = R2 + R3 = (1 + R3/R2) - R1
```

Step 5: Simplify

Rearranging and simplifying, we get:

```
RX = (R2/R1) - R3
```