4.9 PROBLEMS
4.9 Problems 1051 A circuit is supplied from 50 Hz mains whose voltage has a maximum
value of 250 V and takes a current whose maximum value is 5 A. At a
particular instant (t = 0) the voltage has a value of 200 V and the current is
then 2 A. Obtain expressions for the instantaneous values of voltage and
current as functions of time and determine their values at an instant
t = 0.015 s. Determine also the phase difference between them.
2 Three circuit elements are connected in series and the voltages across
them are given by v~ - 50 sin ~ot; v2 = 40 sin (oJt + 60~
v3 = 60 sin (~ot - 30~ Determine the total voltage across the series
combination and its phase angle with respect to Vl.
3 A circuit consists of an inductance of 0.318 H and a resistance of 5 12
connected in series. Calculate the resistance, reactance and impedance
when it operates on a supply of frequency (a) 25 Hz, (b) 50 Hz.
4 A coil of resistance 10 1~ and inductance 47.7 mH is connected to a 200 V,
50 Hz supply. Calculate (a) the current drawn from the supply, (b) the
power factor of the circuit.
5 A capacitor of 50 I~F capacitance is connected in series with a resistance of
50 f~ to a 200 V, 50 Hz supply. Calculate (a) the current drawn from the
supply, (b) the voltage across the resistance, and (c) the voltage across the
capacitance.
6 A capacitor of 80 IxF capacitance takes a current of 1 A when supplied
with 250 V (rms). Determine (a) the frequency of the supply, and (b) the
resistance which must be connected in series with this capacitor in order to
reduce the current to 0.5 A at this frequency.
7 A resistance of 50 l-I is connected in series with a variable capacitor across
a 200 V, 50 Hz supply.
(a) When the capacitance is set to 50 IxF calculate (i) the current drawn
from the supply, (ii) the voltage across the two elements and (iii) the
power factor.
(b) Find the value of the capacitance when the current is 2 A.
(c) Determine the value of the capacitance required to give a power factor
of 0.866 leading.
8 A circuit consists of a 100 f~ resistance in parallel with a 25 I~F capacitor
connected to a 200 V, 50 Hz supply. Calculate (a) the current flowing in
each branch, (b) the total current drawn from the supply, (c) the
impedance of the circuit, and (d) the phase angle of the circuit.
9 A capacitor having a reactance of 5 11 is connected in series with a resistor
of 10 f~. This circuit is then connected (a) in series and (b) in parallel with