Page 369 - Schaum's Outline of Theory and Problems of Applied Physics

354 ALTERNATING-CURRENT CIRCUITS [CHAP. 29

Fig. 29-4

Since we want to work with effective voltages and currents, not instantaneous ones, we must somehow take
into account the phase differences. To do this, we can use phasors to represent the various effective quantities.
This is done in Fig. 29-6 for the voltages. To find the magnitude V of the sum V of the various effective voltages,
we proceed in this way:
1. Find the difference V L − V C .If V L > V C , then V L − V C will be positive and will point upward; if
V L < V C , then V L − V C will be negative and will point downward.
2. Add V L − V C to V R to obtain V. Since V L − V C is perpendicular to V R , use the Pythagorean theorem
to find the magnitude V :

2
V = V + (V L − V C ) 2
R
The angle φ between V and V R is the phase angle and can be calculated from the relationships

V L − V C V R
tan φ = or cos φ =
V R V
SOLVED PROBLEM 29.7

A resistor, a capacitor, and an inductor are connected in series to an ac power source. The effective
voltages across the circuit components are V R = 5V, V C = 10 V, and V L = 7 V. Find (a) the effective