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NUMERICALS
1. Mean, Peak and rms Values of A
C 5. The electric main in a house is marked 220 V-50 Hz.
1. An alternating current is given by I = 50 sin 100 t. Write down the equation for the instantaneous voltage.
Find the frequency of current, mean current during a The only variable in this equation should be t.
positive half-cycle, virtual current and the current at (ISC 2005)
t= (1/300) s. pAns. 50 Hz, 31.8 A, 35.4 A, 43.3 A. Ans. V = 220/2 sin (100 nt).
2. A hot-wire ammeter in an AC circuit reads 10 A (rms 6. The current and voltage in a circuit are given by
value). What is the peak current? Ans. 14.1 A.
I=3.5 sin (628 t +30) ampere, V= 28sin (628t -30°)
3. If the peak alternating current in a circuit is 21.2A, find volt. Determine (i) peak value, (ii) root-mean-square
out the reading of an ammeter connected in the circuit. value, (iii) time-period of the current and (iv) phase
Ans. 15 A. difference between voltage and current.
4. The equation of an AC voltage is vo) Ans. (i) 3.5 A, (ii) 2.47 A, (iii) 0.01 s and (iv) 60°.
V = 10042 sin(100 nt). II. AC Circuit with either of R, L or C
7. What is the self-inductance of a coil if
Find the rms value and the frequency of the voltage. its inductive
Ans. 100 V 50Hz. reactance is 12.56 2 at a frequency of 200 Hz?
Ans. 0.01 H.
, Alternating Current 603
At what
frequency willla 2
8
of 4000 S2?
pure inductor of
Hinductor Ans.
have a
reactance
(1000/) Hz. 20. A bulb of resistance 10 2,
connected to an inductor of
an AC source marked
A 0.5 H
carries an inductance L, is in series with
frequency 50 Hz. What AC angle between the voltage
will the of 0.2 Aand of
ends of the inductor and the be 100V 50 Hz. If the phase find the value of L.
phase voltage across the and the current is n/4 radian,
the voltage and the current? difference between Ans. H.
Ans. 31.4 V 90° 10
Aiton of (current lags behind
10V-70inductance
10 A pure
Hz source. Find1.0 His connected voltage). 21. For the given circuit, 0.1 H 30
across
reactance, current and peak a find (i) the reactance,
value of current.
.. Acapacitor ot S0 pF is Ans. 440 2, 0.25 A, 0.35 A. (ii) the impedance,
(iii) the peak value of
connected to an AC
frequency 1 kHz. Calculate its reactance. source of current and (iv) the
phase difference between V= 10 6in 400t
o A2.0 uF Ans. (10'/) Q.
capacitor is connected to a 220 voltage and current.
ner. source. Calculate the reactance of the V 50 Hz AC (tan 1.33 = 53)
current flowing in the circuit and capacitor, the Ans. (i) 40 2,(iü) 50 2, (iiü) 0.2 A, (iv) 53.
s? mention the phase
relationship between the current and the voltage. 22. An AC circuit has a 100 2
Ans. 1592.3 2, 0.138 A, current leads resistance and an
13, Find the frequency at which the the voltage by 90°. inductance connected
a l.0 uF capacitor equals the capacitive reactance of in series, as shown.
1.0 H coil. inductive reactance of a Calculate the current
Ans. 159.24 Hz.
14. Acoil has an inductance of 1 H. At what and the power factor
it have a reactance of 3140 2? What frequency will in the circuit.
250 V
capacitance will
have the same reactance at that frequency? Ans. 0.1325 A, 0.053.
Ans. 500 Hz, aboutl x 10 E 23. Acurrent of 1.1Aflows through a coil when connected
III. AC Circuit containing R and L toa 110 VDC source. When 110 V-50 Hz AC is applied
15. A 100 V-50 Hz AC source is connected to a series tothe same coil, only 0.5 Acurrent flows. Calculate the
combination of an inductance of 100 mH and a resistance, impedance and inductance of the coil.
resistance of 25 2. Calculate the magnitude and phase Ans. 100 2, 220 2, 0.624 H.
of current. 24. An ACcircuit consists of a 220 V 50 Hz supply connected
Ans. 2.5 A, 51.5° (current lags behind voltage). ocacross a 10 2 resistor. What inductance should be
16. The inductance and resistance of a choke-coil are introduced in the circuit in series with the resistance so
0.2 H and 0.5 2 respectively. A current of 2.0 A (rms) that the current is reduced to half? Ans. 0.55 H.
and frequency 50Hz is passed through it. Nhat will De 25. A coil has a current of 1.0 A and a power of 100 W
the PD across its ends? Ans. 125.6 V. from
an AC source of 110 V and 50 Hz. Find the resistance
17. A non-inductive resistance of 12 2 and an inductance of and the inductance of the coil.
0.05 Hof negligible resistance are connected in series in Hint : P=R.
an AC circuit having frequency 50 Hz and voltage 130 V
Determine impedance and current in the circuit. Ans. Ans. 100 S2, 0.146 H.
19.76 2, 6.58 A. 26 An emf V = 200 sin 377 t volt is applied across an
18. A current of 2.0 A inductance Lhavinga resistance of 1.0 2. The maximum
is flowing in the current is found to be 10 A. Find the value of L.
given L-R circuit. k-240V k-100V Ans. 53 mH.
Find the voltage 27. An electric lamp which runs at 80 VDC, consumes 10 A
across the AC
source and the current. The lamp is connected to 100V-50 Hz AC source.
impedance of the V=V, sin wt Compute the inductance of the choke required.
Ans. 0.02 H.
circuit. IV. AC Circuit containing R and C
Ans. 260 V 130Q.
28. In the given AC
19. An alternating emf of 110 V is applied to a circuit circuit, find out the
X=30a R=409
containing a resistance of 40 2 and an inductance L potential difference H
in series. The current lags behind the emf by an angle across the (i) resistor,
tan n- (3/4). Find the inductive reactance, impedance
of the circuit and current in the circuit. If L=0.1 H, find (i) capacitor.
the frequency of applied emf. Ans. (i) 200 V
250 V
Ans. 30 s2, 50 2, 2.2 A, 300 rad s. (ii) 150 V
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