ASSIGNMENT : ALTERNATING CURRENT
1. The equation of an alternating current is I = 3 √2 sin (100πt + π/
4) .Find the root mean square value and frequency of the current.
2. An open coil inductor L of inductive reactance XL is connected in series
with a bulb B and an a.c. source. How would brightness of the bulb
change when (i) number of turns in the inductor are reduced ? (ii) an
iron rod is inserted into the interior of the inductor ? (iii) a capacitor of
capacitive reactance XC = XL is connected in series in the circuit ?
3. An ideal inductor of 5 /π H inductance is connected to a 200 V, 50 Hz
ac supply. (a) Calculate the rms and peak value of current in the
inductor. (b) What is the phase difference between current trhough the
inductor and the applied voltage ? How will it change if a small
resistance is connected in series with this inductor in the circuit?
4. A capacitor behaves as perfect conductor for high frequency a.c.
Explain why ?
5. The instantaneous emf and current equations of an RLC series circuit
are e = 200 sin( ωt +π/ 6) i = 20 sin( ωt -π/ 6) , find the average
power consumed per cycle.
6. For L-C-R A.C. circuit resonance frequency is 600 Hz and frequencies at
half power points are 550 Hz and 650 Hz. What will be the QFactor ?
7. Current of 50/π Hz frequency is passing through an A.C. circuit having
series combination of resistance R = 100 Ω and inductor L = 1H, then
find phase difference between voltage and current i.
8. A series combination of an inductor (L), capacitor (C) and a resistor (R)
is connected across an ac source of emf of peak value E0 and angular
frequency (ω). Plot a graph to show variation of impedance of the
circuit with angular frequency (ω).
9. A resistor R and an inductor L are connected in series to a source of
voltage V = Vo sin ωt. The voltage is found to lead current in phase by
π/4. If the inductor is replaced by a capacitor C, the voltage lags behind
current in phase by π/4. When L, C and R are connected in series with
the same source, Find the : (i) average power dissipated and (ii)
instantaneous current in the circuit.
10. (i) Figure below showx series a series L-C-R circuit connected to
an AC source which generates an alternating emf of frequency of 50
Hz. The reading of voltmeters V1 and V2 are 80 V and 60V
respectively. Find (a) the current in the circuit. (b) the capacitance C of
the capacitor. (ii) At resonance, what is the relation between
impedance of series L-C-R circuit and its resistance R ?
11. An alternating emf of frequency 50 Hz is applied to a circuit with
a resistor of 20Ω, an inductor of 100 mH and a capacitor of 30 µF
connected in series. (i) What is the angle by which the current leads or
lags the applied emf ? (ii) Represent the voltage and the current in a
vector diagram showing the phase angle.
12. In series LCR circuit in which R = 3Ω, L = 25 mH and C = 800 µF
a sinusoidal a.c voltage of peak value 250V is applied. Find (i)
frequency at which resonance occurs (ii) current in the circuit at
resonant condition
13. Define wattless current. In a circuit, when 100 volt e.m.f. is
applied, one ampere current flows. If the phase difference between
current and electromotive force is π/ 3 , calculate
(i) power factor (ii) average power in the circuit (iii) root mean
square value of wattless current.
14. Prove that a high frequency a.c. can pass through a pure
capacitor but not through a pure inductor. When 200V d.c. is applied
across a coil, a current of 2A flows through it. When 200V a.c. of 50 Hz
is applied to the same coil, only 1 A flows through it. Calculate the
resistance (R), impedance (Z) and inductance (L) of the coil.
15. (a) What do you understand by 'sharpness of resonance' for a
series LCR resonant circuit? How is it related with the quality factor 'Q'
of the circuit? Using the graphs given in the diagram, explain the
factors which affect it. For which graph is the resistance (R) minimum?
