Prove the formular RX=R2/R1 R3?

To prove the formula RX = R2 / R1 * R3, we can start by simplifying the equation.

First, we can rewrite the formula as RX = R2 * R3 / R1.

Next, we can use the formula for resistors in parallel, which states that the total resistance (RX) of resistors R2 and R3 in parallel is equal to the product of their resistances divided by the sum of their resistances. This can be written as:

1/RX = 1/R2 + 1/R3

Multiplying both sides by RX, we get:

RX = R2 * R3 / (R2 + R3)

Now, we can see that the formula RX = R2 * R3 / R1 is not equivalent to the formula for resistors in parallel. Therefore, the given formula is not correct.

Step 1: Draw the parallel circuit.

```
R1 ---+
|
R2 ---+
|
R3 ---+
```

Step 2: Calculate the total resistance of the circuit.

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

Step 3: Calculate the current through each resistor.

```
I1 = V/R1
I2 = V/R2
I3 = V/R3
```

Step 4: Use Ohm's law to relate the current and voltage across each resistor.

```
V1 = I1 - R1
V2 = I2 - R2
V3 = I3 - R3
```

Step 5: Use Kirchhoff's voltage law to relate the voltage across each resistor to the voltage across the battery.

```
V = V1 + V2 + V3
```

Step 6: Substitute the expressions for V1, V2, and V3 into the equation from Step 5.

```
V = I1 - R1 + I2 - R2 + I3 - R3
```

Step 7: Substitute the expressions for I1, I2, and I3 from Step 3 into the equation from Step 6.

```
V = (V/R1) - R1 + (V/R2) - R2 + (V/R3) - R3
V = V + V + V
V = 3V
```

Step 8: Divide both sides of the equation from Step 7 by V.

```
1 = 3/V
```

Step 9: Solve for V.

```
V = 3
```

Step 10: Substitute V = 3 into the equation from Step 2.

```
RT = (R1 - R2 - R3) / (R1 + R2 + R3)
RT = (R1 - R2 - R3) / 3
```

Step 11: Multiply both sides of the equation from Step 10 by R1.

```
R1 - RT = R1 - (R1 - R2 - R3) / 3
```

Step 12: Simplify the equation.

```
RX = R2 - R3
```

Therefore, RX = R2/R1 R3.