Question 1.9: Given 10 resistors in parallel of equal value, find the para...

a Using Equation (1.43) for “n = 10” resistors in parallel, we find that

1/R_{parallel-equiv}=1/R_{1}+1/R_{2}+1/R_{3}+….+1/R_{n}.      (1.43)

1/R_{parallel-equiv}=1/R+1/R+1/R+…+1/R          (1.47)

where Equation (1.43) has 10 equal terms because all 10 resistors have the same value.

  From Equation (1.43), we obtain

1/R_{parallel-equiv}=10/R     (1.48)

or

R_{parallel-equiv}=R/10    (1.49)

b Using Equation (1.43) one more time, we obtain

1/R_{parallel-equiv}=1/1+1/1000   (1.50)

from where we obtain that

R_{parallel-equiv}=1000/1001=0.999001 \Omega   (1.51)

Corollary from Example 1.9
The parallel of one resistor with another one that is several orders of magnitude larger than the first one is approximately equal to the smaller resistor value.