Methods of adding alternating waveforms 285
(b) the frequency of the supply.
7. If the supply to a circuit is v = 20 sin 628.3t
volts and the voltage drop across one of
the components is v 1 = 15 sin(628.3t − 0.52)
volts, calculate
(a) the voltage drop across the remainder of
the circuit, given by v − v 1 , in the form
A sin(ωt ± α)
(b) the supply frequency
(c) the periodic time of the supply.
8. The voltages across three components in a
series circuit when connected across an a.c.
supply are v 1 = 25 sin
300πt +
π
6
volts,
v 2 = 40 sin
300πt −
π
4
volts and
v 3 = 50 sin
300πt +
π
3
volts. Calculate
(a) the supply voltage, in sinusoidal form, in
the form A sin(ωt ± α)
(b) the frequency of the supply
(c) the periodic time.