Ham Radio General Class Practice Test

For three resistors in parallel producing a total resistance of 50 ohms, if they are connected in series, how much resistance do they produce?

1. 150 ohms

2. 450 ohms

3. 250 ohms

4. 350 ohms

The correct answer is: 450 ohms

When resistors are connected in parallel, the total resistance can be found using the formula for parallel resistance, which states that the reciprocal of the total resistance is the sum of the reciprocals of the individual resistances. In this case, it is given that three resistors in parallel yield a total resistance of 50 ohms. When resistors are connected in series, the total resistance is simply the sum of the individual resistances. For three resistors in parallel yielding 50 ohms, if we think of these three resistors as equal (for the sake of this explanation), we can denote each resistor as R. In parallel, the equation would apply as \( 1/R_{total} = 1/R + 1/R + 1/R \), which simplifies to \( R_{total} = R/3 \). Therefore, if we assume the individual resistance is 150 ohms (since \( 150/3 = 50 \)), when these three resistors are connected in series, the total resistance becomes: \[ R_{total\_series} = R + R + R = 150 + 150 + 150 = 450 \text{ ohms} \] Hence, when the three resistors that