1. A single phase induction motor is connected to
a 240 volt 50Hz supply and draws 15A at 0.6
power factor. What size capacitor is required
to improve the power factor to 0.85 lagging?

3. Find Φ
pf = cos Φ
Φ = cos¯¹ pf
Φ 1 = cos¯¹ 0.6
= 53.13⁰
Φ 2 = cos¯¹ 0.85
= 31.79⁰

4. Apparent power (S) = VI
=
240 x 15
=
3600 VA

5. True Power (T) = VI COS φ1
= 240 x 15 x 0.6
= 2160 W

6. Motor reactive power (Q)
= VI SIN φ1 (53.13⁰)
= 240 x 15 x 0.8
= 2880 VAR

7. Total reactive power
(Q)
= true power (P) x TAN φ2
= P tan 31.79⁰
= 2160 x .619
= 1338.73 VAR