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680 ⏐⏐⏐ SERIES AND PARALLEL ac CIRCUITS
+
e
–
R
L
+
vL –
Oscilloscope
FIG. 15.97
Determining the phase relationship between e and v L.
θ
1.6 div.
e
T = 8 div.
FIG. 15.98
Determining the phase angle between e and v L.
For the chosen horizontal sensitivity, each waveform of Fig. 15.98
has a period T defined by eight horizontal divisions, and the phase angle
between the two waveforms is defined by 1 �1
2 � divisions. Using the fact
that each period of a sinusoidal waveform encompasses 360°, the following
ratios can be set up to determine the phase angle v:
v
� 8 div.
� � �
360°
1.6 div.
�
v
and v � � � 360° � 72°
In general,
1.6
�
8
( div.
for
v)
v � � � � 360°
( div.
for
T)
1
2
a c
(15.43)
If the phase relationship between e and v R is required, the oscilloscope
must not be hooked up as shown in Fig. 15.99. Points a and b
have a common ground that will establish a zero-volt drop between the
two points; this drop will have the same effect as a short-circuit connection
between a and b. The resulting short circuit will “short out” the
inductive element, and the current will increase due to the drop in
impedance for the circuit. A dangerous situation can arise if the inductive
element has a high impedance and the resistor has a relatively low