Chapter 6, Problem 36P

Parts (a) through (e) of this problem should be done by inspection—that is, mentally. The intent is to obtain an approximate solution without a lengthy series of calculations. For the network in Fig. 6.98:

1. What is the approximate value of $l_1$, considering the magnitude of the parallel elements?
2. What is the ratio ${\text{l}}_{\text{1}}{\text{/l}}_{\text{2}}?$
3. Based on the result of part (a), what is an approximate value of $l_2?$
4. What is the ratio ${\text{l}}_{\text{1}}{\text{/l}}_{\text{3}}?$
5. Based on the result, what is an approximate value of $l_3?$
6. What is the ratio ${\text{l}}_{\text{1}}{\text{/l}}_{\text{4}}?$
7. Based on the result, what is an approximate value of $l_4?$
8. What is the effect of the parallel $100\text{kΩ}$
9. resistor on the above calculations? How much smaller will the current $l_4$
10. be than the current $l_1$
11. ?
12. Calculate the current through the $1\text{KΩ}$
13. resistor using the current divider rule. How does it compare to the result of part (a)?
14. Calculate the current through the $10\Omega$
15. resistor. How does it compare to the result of part (b)?
16. Calculate the current through the $1\Omega$
17. resistor. How does it compare to the result of part (c)?
18. Calculate the current through the $100\text{KΩ}$
19. resistor. How does it compare to the solutions to part (e)?