Problem 4-67
Find io
and vo when
Ro is 0 W,
2 W, 6 W,
10 W, 15 W,
20 W, 30 W,
40 W, 50 W,
and 70 W.
The easiest way to solve for multiple values
of Ro is to find the Thevenin
equivalent of the entire circuit excluding Ro,
then connect the various values of Roto
the Thevenin equivalent. The simplest method for finding the Thevenin
equivalent is probably circuit reduction, although you could also
find voc and isc
using nodal or mesh analysis.
Circuit reduction:
Transform the violet elements.
Combine current sources in parallel and resistors (10 W and 40 W)
in parallel.
Transform the violet elements, then add the 8 W
and 2 W resistors which are then in
series (intermediate step not shown).
Now it is very straightforward to calculate io
and vo for the various values
of Ro.
Using voltage division, we get
vo = 120 Ro
/ (10 + Ro)
From Ohm's Law we get
io = 120
/ (10 + Ro)
(or you could get io first,
then calculate vo using Ohm's
Law: vo = Ro
io.)
Thus the results are
- Ro.= 0 W,
vo = 0 V, io
= 12 A
- Ro.= 2 W,
vo = 20 V, io
= 10 A
- Ro.= 6 W,
vo = 45 V, io
= 7.5 A
- Ro.= 10 W,
vo = 60 V, io
= 6 A
- Ro.= 15 W,
vo = 72 V, io
= 4.8 A
- Ro.= 20 W,
vo = 80 V, io
= 4 A
- Ro.= 30 W,
vo = 90 V, io
= 3 A
- Ro.= 40 W,
vo = 96 V, io
= 2.4 A
- Ro.= 50 W,
vo = 100 V, io
= 2A
- Ro.= 70 W,
vo = 105 V, io
= 1.5 A
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