A pure resistance of 50 ohms is in series with a pure capacitance of 100 micro farads. The series combination is connected across 100-V, 50-Hz supply. Find (a) the impedance (b) current (c) power factor (d) phase angle (e) voltage across resistor (f) voltage across capacitor. Draw the vector diagram.
XC = 106 π /2π × 50 × 100 = 32 Ω ; R = 50 Ω
(a) Z = √(502 + 322) + 59.4 Ω
(b) I = V/Z = 100/59.4 = 1.684 A
(c) p.f. = R/Z = 50 = 59.4 = 0.842 (lead)
(d) φ = cos−1 (0.842)= 32°36′
(e) VR = IR = 50 × 1.684 = 84.2V
(f) VC = IXC = 32 × 1.684 = 53.9V
