1) Find an expression for the equivalent resistance of 2 resistors of value R in

Question

1) Find an expression for the equivalent resistance of 2 resistors of value R in series.
2) Find an expression for the equivalent resistance of n resistors of value R in series.
3) Using the results of (1) design a resistive network with an equivalent resistance of 3 kohms using 2 resistors with the same value from those: 1k, 1.2k, 1.5k, 1.8k, 2.2k, 2.7k, 3.3k, 3.9k, 4.7k, 5.6k, 6.8k.
4) Using the results of (2), design a resistive network with an equivalent resistance of 4k using a minimum number of identical resistors from those given above.

Thank you!

Explanation / Answer

1) R1=R; R2=R

     R1+R2=2R

2)R1=R; R2=R; ...Rn=R

    R1+R2+...+Rn= nR

3)R1+R2= 2R

    3.0k= R1+R2= 1.5k+1.5k

4)R1+R2+...+Rn= nR

    Let n=4.

    nR=4.0k; R=1.0k

    Now verify that n is minimum. (Check that n=1,2,3 does not work.)

    Let n=3. nR=4.0k; R=1.33k This does not work.

    Let n=2. nR=4.0k; R=2.0k This does not work.

    Let n=1. nR=4.0k; R=1.0k This does not work.

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