Question

Given only one 10 and one 85 resistor, list all possible values of resistance that can be obtained. (Give values in ascending order. Enter 'none' in all remaining unused answer boxes, if any.) there are 5 box's

Answer 1

If we assume that the option exists to only use 1 resistor at a time, we can have up to 4 different combinations.
10 ohms
85 ohms
Series equivalent resistance
Parallel equivalent resistance

In a series circuit, all resistive elements see the same current as there is only one path for the current to travel. With this as the case the resistances in a series circuit simply add. Thus 10 + 85 = 95 ohms.

For our last consideration, a parallel circuit is not so direct in the determination of the resistance. To find what is called the "Equivalent Resistance" in a parallel circuit, we use the following equation:

\[R _{eq} = \frac{ 1 }{ \frac{ 1 }{ R _{1}}+\frac{ 1 }{ R _{2} } +...+\frac{ 1 }{ R _{n} }}\]
This is described as finding the "Inverse of the sum of the inverses." In our case we would need to only consider the 10 and 85 ohm. 1/10 yields 0.1. 1/85 yields 0.01176. Thus\[R_{eq} = \frac{ 1 }{ 0.1+0.01176 } = \frac{ 1 }{ 0.11176 } = 8.95 Ohms\]

So ranking in order from least to greatest:
8.95 Ohms
10 Ohms
85 Ohms
95 Ohms

Answer 2

thank you so much for your help:)

Answer 3

You're welcome.