Basic Engineering Mathematics, Fifth Edition

Methods of adding alternating waveforms 285

(b) the frequency of the supply.

7. If the supply to a circuit isv=20sin628. 3 t
   volts and the voltage drop across one of
   the components isv 1 =15sin( 628. 3 t− 0. 52 )
   volts, calculate

(a) the voltage drop across the remainder of

the circuit, given byv−v 1 , in the form

Asin(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 =25sin

(

300 πt+

π

6

)

volts,

v 2 =40sin

(

300 πt−

π

4

)

volts and

v 3 =50sin

(

300 πt+

π

3

)

volts. Calculate

(a) the supply voltage, in sinusoidal form, in

the formAsin(ωt±α)

(b) the frequency of the supply

(c) the periodic time.