İzmir University of Economics
CE 205 Fundamentals of Electrical Circuits Lab
LO-8 (Part 2)
Analyze R-L-C circuits using phasors
Preliminary
1. Prove that
T
T
1
i.
0 cos ω t dt = 0 where ω=2πf, f = T , i.e., cos dt = 0
ii.
T
0 sin ω t
iii.
iv.
dt = 0 where ω=2πf, f =
1
,
T
T
0 cos (ω t +θ) dt = 0 where ω=2πf, f
T
1
0 cos 2ω t dt = 0 where ω=2πf, f = T
0
T
i.e., sin dt = 0
=
1
T
0
Basic
1. Consider the circuit given. Assume PL is the power
dissipated over RL.
(a) Determine PL when RL = 2 Ω.
(b) Determine PL when RL = 6 Ω.
(c) What is the value of RL when maximum power
is dissipated over RL?
(d) Determine the maximum power PL(max).
4Ω
10 V
RL
2. Consider the circuit given. The input voltage is
cosine given as
vin (t) = 10 cos 10 t volts
(a)
(b)
(c)
(d)
Determine the phasor Vin of vin .
Draw the phasor equivalent circuit.
Determine the phasor VO of vO .
Determine the voltage vO(t) at steady state.
+
2Ω
0.1 F
vin
vo
4Ω
0.05 F
-
3. Consider the circuit given. The voltage input is the
sum of two sinusiodals. Calculate the intantaneous
and average power dissipatation over the resistor
when,
(a) vs (t) = 2 cos 2ωt + cos ωt volts
(b) vs (t) = cos ωt + 2 sin ωt volts
(c) vs (t) = 2 cos 2ωt + sin ωt volts
vs(t)
R
9-1
4. Assume the voltage across and the current through an
impedance is measured as
v(t) = VP cos ( ω0 t + θ1 ) volts
i
+
v
-
and
i(t) = IP cos ( ω0 t + θ2 ) amperes
Z
(a) Show that the instaneous power dissipation over this
impedance is
Pinst (t) =
VP IP
' cos( 2 ω0 t + θ1 +θ2 ) + cos( θ1 - θ2 ))
(b) Show that the average power is
Pavg (t) =
where ω0 =
1 T
V I
P (t) dt = P P
T 0 inst
2π
T
cos θ
and the phase difference θ = θ1 - θ2
5. Consider the circuit given. The input voltage is given as
+
vin (t) = 8 cos 10t volts
vout
vin
Determine the output voltage vout at steady state.
-
√3 Ω
0.1 F
Intermediate
6. Consider the circuit given.
(a) Determine the frequency transfer function
H(jω) as the ratio of output to input
phasors.
V
H(jω) = out
Vin
(b) Determine the magnitude and phase
functions
R1
vin
C
C
R1
+
-
vout
9-2
7. Consider the circuit given. The input voltage is
given as
vin (t) = 2 cos 5t volts
-
vout
2Ω
Determine the output voltage vout(t) at steady
state.
+
2 cos 5t
volts
5Ω
0.1F
2
2Ω
8. Consider the circuit given. Find the
values of R and L such that
maximum power is transferred to
the load.
2 cos 5t
volt
ZL
R
0.1 F
L
Advanced
9. Consider the circuit given. Determine the
average power supplied by the current source.
+
2 cos 5t
ampere
vS
5Ω
1H
-
10.
Consider the circuit given.
(a) Show that
R7 C =
R1
8
9:
is required for maximum power
to be transferred to the load.
(b) Express R2 and L in terms of R1
and C when maximum power is
transferred to the load.
cos ω0t
volt
C
ZL
R2
L
9-3