Question

Suppose that you have a 680 Ω, a 720 Ω and a 1.20 kΩ resistor. (a) What is the maximum resistance you can obtain by combining these? (b) What is the minimum resistance you can obtain by combining these?

Answer 1

Explanation:

As the given data is as follows.

    $R_{1} = 680 \ohm$ ohm$\ohm$,    $R_{2} = 720 \ohm$ ohm,

   $R_{3} = 1.2 k\ohm$ = 1200 $\ohm$   (as 1 k ohm = 1000 m)

(a)   We will calculate the maximum resistance by combining the given resistances as follows.

      Max. Resistance = $R_{1} + R_{2} + R_{3}$

                                  = $(680 + 720 + 1200) \ohm$ ohm

                                  = 2600 ohm

or,                               = 2.6 $k\ohm$ ohm

Therefore, the maximum resistance you can obtain by combining these is 2.6 $k\ohm$ ohm.

(b)   Now, the minimum resistance is calculated as follows.

      Min. Resistance = $\frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}}$

                                 = $\frac{1}{680} + \frac{1}{720} + \frac{1}{1200}$

                                 = $3.683 \times 10^{-3}$ ohm

Hence, we can conclude that minimum resistance you can obtain by combining these is $3.683 \times 10^{-3}$ ohm.