(a) If Rout 3 k Ω, find the power delivered to it. (b) What is the maximum power that can be delivered to any Rout? (c) What two different values of Rout will have exactly 20 mW delivered to them?
Answers
Answer:
Power Transfer Theorem
Dr. L. Joyprakash Singh
Solution:
We first find the Th´evenin equivalent of the network when
R
out
is removed in the givencircuit. Thus, we have the network in which Th´evenin equivalent is to be obtained as shown in Fig. 1(a).Removal of
R
out
left us with a single mesh in thenetwork and if the clockwise mesh current is
i
1
,2000
i
1
+ 20 + 30 + 2000
i
1
= 0
⇒
i
1
=
−
12
.
5
mA
Therefore, the
V
TH
=
−
40 + 30 + 2000
i
1
=
−
40
−
20 + 2000
i
1
.
2kΩ
+
−
20V2kΩ
+
−
30V
+
−
40V
Fig. 1(a): When
R
out
is removed.
Thus
V
TH
=
−
40 + 30 + 2000
×−
12
.
5
×
10
−
3
=
−
35
V
Now shorting the independent sources of the net-work Fig. 1(a)
R
TH
= 2000
||
2000 = 1
k
Ω
2kΩ2kΩ
R
TH
Fig. 1(b): After suppressing all voltage sourcesof Fig. 1(a).
Then, we can solve subparts of the question asa) With
R
out
= 3
k
Ω in the network of Fig. 1(c)
V
R
out
= 31 + 3
×−
35 =
−
26
.
25
V
∴
p
R
out
=
v
2
R
out
R
out
= (
−
26
.
25)
2
3000
⇒
p
R
out
= 229
.
6875
mW .
+
−
V
TH
=
−
35
V R
TH
=1
k
Ω
R
out
+
v
L
−
i
L
Fig. 1(c): Simplified network of Fig. 1.
b) Maximum power is delivered to
R
out
of Fig. 1(c) when
R
out
=
R
TH
is
p
max.
=
v
2
R
out
R
out
=
10001000 + 1000
×−
35
2
1000 = 305
.
251000 = = 306
.
25
mW .
where
v
R
out
using voltage division method
v
R
out
=
R
out
R
TH
+
R
out
×
V
TH
c) We know20
×
10
−
3
=
v
2
R
out
R
out
where
v
R
out
=
R
out
R
TH
+
R
out
V
TH
=
R
out
1000 +
R
out
×−
35
∴
20
×
10
−
3
= 35
2
(1000 +
R
out
)
2
×
R
out
.
ECE, NEHU, Shillong
−
22 Page 2 of 4 September 23, 2015