Your electronic friend needs a 20 ohms resistor but has only 40 ohms resistor. He tells you that he can combine them to produce a 20 ohms resistor? How?

If you have two 40 ohms, arrange them in parallel.

If you have one, you are out of luck.

To combine resistors in order to obtain a different resistance value, you can use two formulas known as the series and parallel resistor equations.

In this case, your electronic friend needs a 20 ohms resistor but only has a 40 ohms resistor. To obtain a 20 ohms equivalent resistance, you can achieve this by combining the resistors in series.

Let's explain how to calculate the equivalent resistance when resistors are connected in series:

1. Series connection: When resistors are connected in series, their resistances add up. The formula to calculate the equivalent resistance (Rs) for resistors in series is:

Rs = R1 + R2 + R3 + ... (where R1, R2, R3, ... represent the individual resistances)

To obtain a 20 ohms resistor using a 40 ohms resistor, you can calculate the required additional resistance value using the series resistor equation:

Rs = R1 + R2
20 ohms = 40 ohms + R2

If you rearrange the equation to solve for R2 (the additional resistance needed), you get:

R2 = 20 ohms - 40 ohms
R2 = -20 ohms

This calculation indicates that you would need a negative resistance, which is not physically possible. Therefore, it is not possible to obtain a 20 ohms resistor by combining a 40 ohms resistor in series.

In this scenario, your electronic friend would need to obtain a resistor with the correct resistance value of 20 ohms.