1.3 KIRCHHOFF’S LAWS 39
(b) By voltage division [see Figure E1.2.6(c)] one gets
v′L=
1800
1800 + 1800
( 10
√
2 sin 2t)=( 5
√
2 sin 2t)V
which has an rms value of 5 V. Hence, the average power delivered to the load resistance
(R′LorRL)is
Pav=
(VL′RMS)^2
1800
=
25
1800
W∼= 13 .9mW
Note thatvLacrossRLis( 5
√
2 / 6 )sin 2tV, andiLthroughRLis( 5
√
2 / 6 × 50 )sin 2t
A. The rms value ofiLis then 5/300 A, and the rms value ofvLis^5 / 6 V. Thus,
Pav=
5
300
×
5
6
W∼= 13 .9mW
which is also the same as
Pav=IL^2 RMSRL=VL^2 RMS/RL
−
+ RS
v RL
(a)
υL′ υL
−
+
RS = 1800 Ω
10 2 sin 2t V RL = 50 Ω
iLN 1 N 2 iL
Ideal transformer
(b)
Source Load
+
−
+
−
′ :
υL′ ′
−
+
RS = 1800 Ω
10 2 sin 2t V RL =^1800 Ω
iL
(c)
+
−
′
Figure E1.2.6
1.3 Kirchhoff’s Laws
The basic laws that must be satisfied among circuit currents and circuit voltages are known as
Kirchhoff ’s current law(KCL) andKirchhoff ’s voltage law(KVL). These are fundamental for
the systematic analysis of electric circuits.
KCL states that, at any node of any circuit and at any instant of time, the sum of all currents
entering the node is equal to the sum of all currents leaving the node. That is, thealgebraicsum of
