Question

A 33-kΩ resistor is connected in series with a parallel combination made up of a 56-kΩ resistor and a 7.8 kΩ resistor. What is the total combined resistance of these three resistors? A. 33 kΩ B. 56 kΩ C. 7.8 kΩ D. 26.5 kΩ

Answer 1

The total combined resistance of the three resistors is 39.84 kΩ.

Step-by-step explanation:

The total combined resistance of the three resistors can be found by adding the resistance of the series resistor to the equivalent resistance of the parallel combination. Let's calculate it step by step:

1. The resistance of the series resistor is 33 kΩ.
2. The equivalent resistance of the parallel combination is given by the formula: 1/Rp = 1/R1 + 1/R2, where R1 = 56 kΩ and R2 = 7.8 kΩ. Plugging in the values, we get: 1/Rp = 1/56 + 1/7.8 = 0.01786 + 0.1282 = 0.1461. Taking the reciprocal, we find Rp = 6.84 kΩ.
3. The total combined resistance is obtained by adding the series resistance and the parallel equivalent resistance: Rt = 33 kΩ + 6.84 kΩ = 39.84 kΩ.

Therefore, the total combined resistance of the three resistors is 39.84 kΩ.