Download theory question on ac circiut

THEORY QUESTION ON AC
CIRCIUT
1. Define the following:
I. Reactance
II. Impedance
Solution:
I. Reactance is the opposition in ohms to
the alternating current by an inductor, a
capacitance or both.
Reactance in an AC circuit X, is the
ratio of the peak voltage Vo to the peak
current Io through a capacitor or an
inductor. It is measured in ohms (Ω).
II. Impedance is the total opposition in
ohms to the alternating current by a
combination of resistor as well as a
capacitor or an inductor.
Impedance in an AC circuit Z is the ratio
of the peak voltage
Vo to the peak current Io through an AC
circuit containing the reactances (either
capacitive or inductive, or both) and
resistance.
2. Explain resonant frequency of an
RLC Circuit.
Solution:
Resonant frequency f o is the tendency
at which the current in the circuit has a
maximum value f o 
1
2 LC
3. Explain this statement - the power
supply voltage of a source is 230V.
Solution:
It means that the root mean square
(r.m.s) value of a voltage is 230V
4. A source of Emf 240V & a frequency
of 50Hz are connected to a series
arrangement of a resistor, an inductor &
a capacitor. When the current in the
capacitor is 10A, the potential difference
across the resistor is 140V & that across
the inductor is 50V. Calculate
(i.) The potential difference across
the capacitor;
(ii.) capacitance of the capacitor;
(iii.) inductance of the inductor;
(iv.) draw & label one vector diagram
for the potential difference across
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the inductor, the capacitor & the
resistor.
XC
II .
?
1
wC
1

2fC
V
 C
IC
Solution:
XC 
Emf = 240V; f = 50Hz;
VR  140V ; VL  50V ; I C  10 A ; VC  ? ;
XC
X L  ?; X C  ?; L  ?; C  ?
Note that same current passes through
RLC circuit. Therefore, I C  I R  I L  10 A .
I. VC can be gotten by using
Emf 2  VR2  (VL  VC ) 2
2402  1402  (50  VC ) 2
57600  19600  (50  VC ) 2
57600 19600  50  VC
38000  50  VC
 VC  194.95  50
 VC  144.95
VC  145V
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XC
VC
1

IC
2fC
C
IC
2fVC
10
( 2)(3.14)(50)(144.95)
10
C
45514.3
C  0.0002197 F
C
C  219.7  10  6 F
C  219.7 F
C  220 F
XL
III .
 wL
X L  2fL
XL 
VL
IL
VL
 2fL
IL
L
VL
2fI L
50
( 2)(3.14)(50)(10)
50
 0.0159 H
L
3140
L  15.9mH
L  16mH
L
the capacitor;
(ii.) The capacitance of the capacitor;
(iii.) The inductance of the inductor.
[Take ∏ = 3.14]
Solution:
Emf = V = 110V; f = 60Hz;
IC = 2A; VR = 80V;
VC = ?;
C=?
VL = 40V
XL = ? ;
XC = ?
L =?;
Take note that the same current passes
through the three devices in the RLC
circuit.
The diagram is below:
IV.
VL
VECTOR DIAGRAM
C
R
VR
VL
VR
VL
V
VC
I.
5. A source of emf 110V & frequency
60Hz is connected to a resistor, an
inductor & a capacitor in series. When
the current in the capacitor is 2A, the
potential difference across the resistor is
80V & inductor is 40V.
Draw the diagram of the potential
differences across the inductor, capacitor
& the resistor.
Calculate
(i.) The potential difference across
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V 2  VR  (VL  VC ) 2
2
110 2  80 2  (40  VC ) 2
110 2  80 2  (40  VC ) 2
5700  (40  VC ) 2
Square  root
5700  40  VC
75.498  40  VC
VC  35.498V
| VC | 35.5V
VC
II.
XC 
VC
1

I C 2fC
IC
C
2fVC
C
2
(2)(3.14)(60)(35.498)
2
C
13375.6464
C  0.0001495F
6
C  1149.5  10 F
C  150.0F
6. In a series RC circuit, the resistance
of the resistor is 4Ω, the capacitive
reactance is 3Ω. Determine the
impedance of the circuit.
Solution:
R = 4Ω;
Z 2  R 2  X C2
Z 2  4 2  32
Z 2  16  9
Z 2  25
Z  25
Z  5
III.
XL 
VL
 wL  2fL
IL
VL
 2fL
IL
L
VL
2fI L
40
( 2)(3.14)( 60)( 2)
40
L
753.6
L  0.05307856 H
L
L  53.1  10 3 H
L  53.1mH
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XC = 3Ω
7. The current I in an AC circuit is given
by the equation I  30Sin100t where t is
the time in seconds. Deduce the
following from the equation:
I. Frequency of the current
II. Peak value of the current
III. RMS value of the current.
Solution:
I  30 Sin100t
Equate  with
I  I 0 Sinwt
Where...
I 0  30 A; w  100
I.
w  2f  100
f  100
2
f  50 Hz
II .
I 0  30 A
I rms
III .
I
 0
I rms  30
I rms
2
2
 21.21A
Compiled and edited
by:
FABIYI Clement O.
[email protected]
http://facebook.com/sum
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