Question

What are the largest and smallest resistances you can obtain by connecting a 36.0-Ω , a 50.0-Ω , and a 700-Ω resistor together?

Answer 1

Answer:

786Ω and 20.32Ω respectively.

Explanation:

(a) Given a number of resistors each with its own resistance, the largest resistance can be obtained when these resistors are connected in series.

From the question, the resistors have the following resistances;

36.0-Ω, 50.0-Ω , and 700-Ω

Now, when they are connected in series, the total resistance (R) obtainable is given by the sum of these individual resistances as follows;

R = 36.0-Ω + 50.0-Ω + 700-Ω

R = 786Ω

Therefore, the largest resistance that can be obtained by connecting  a 36.0-Ω , a 50.0-Ω , and a 700-Ω resistor together is 786Ω

(b) Similarly, given a number of resistors each with its own resistance, the smallest resistance can be obtained when these resistors are connected in parallel.

From the question, the resistors have the following resistances;

36.0-Ω, 50.0-Ω , and 700-Ω

Now, when they are connected in parallel, the total resistance (R) obtainable is given by using the relation as follows;

$\frac{1}{R}$ = $\frac{1}{36.0}$ + $\frac{1}{50.0}$ + $\frac{1}{700.0}$

$\frac{1}{R}$ = $\frac{35000+25200+1800}{1260000}$

$\frac{1}{R}$ = $\frac{62000}{1260000}$

$\frac{1}{R}$ = $\frac{62}{1260}$

R = $\frac{1260}{62}$

R = 20.32Ω

Therefore, the smallest resistance that can be obtained by connecting  a 36.0-Ω , a 50.0-Ω , and a 700-Ω resistor together is 20.32Ω