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Mathematics-Online problems:

Solution to the problem of the (previous) week

Problem:

In a series connection of resistors the total resistance is equal to the sum of the individual resistances, whereas in a parallel connection the reciprocal value of the total resistance is equal to the sum of the reciprocal values of the individual resistances. The figure shows an example:

\includegraphics{widerstand_en}

  1. How many different total resistances can be implemented by combining four 10-$ \Omega$ resistors?

  2. State the nine smallest values of resistance in ascending order.


Answer:



  2. $ \Omega$
    $ \Omega$
    $ \Omega$
    $ \Omega$
    $ \Omega$
    $ \Omega$
    $ \Omega$
    $ \Omega$
    $ \Omega$

    (The results should be correct to three decimal places.)

Solution:

Altogether, there are 10 possibilities to construct a circuit diagram with four resistors, but one value of resistance occurs twice:


\includegraphics{skizzen_en}

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