Table of Contents
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This vector circuit matching quiz will hurt the brain a little more
than most of the ones that were printed in Popular Electronics.
In order to score well, it helps to visualize the circuits relative
to where they would appear on a Smith Chart. Capacitive impedances
lie in the bottom half and have negative phases (-s, -jω).
Inductance lie in the upper half and have positive phases (s, jω).
The familiar 'ELI
the ICE man' mnemonic helps, too. Be sure to pay attention to
the color of the vector arrow heads.
Example: In a purely inductive circuit like #4, voltage leads
current by 90°. Since phase rotation is CCW, you need to look
for lettered phase diagram where the white arrowhead (voltage) is
90° ahead of the black arrow head (current), going in the CCW direction.
Vector diagram later 'H' looks like that. Circuit #10, being purely
capacitive, is just the opposite, so its vector diagram is...? Resistance
in parallel or series with reactance adjusts the phase angle somewhere
between 0° and 90° (not lying on an axis
line). The rest are combinations thereof.
Vector-Circuit Matching Quiz
By Robert P. Balin
Vector diagrams are widely used to show the magnitude and phase
relationships between voltages and currents in an a.c. circuit.
A knowledge of vectors is a must for understanding the theory behind
frequency modulation and detection, color TV and feedback circuits.
Ten circuits (1-10) are shown below; vector diagrams (A-J) representing
the voltages and currents in the circuits are also shown. To test
your knowledge of vectors, match the diagrams to the circuits. Note
that this is a simple matching quiz - obviously special cases might
exist if the effects of resonance were considered. It is also assumed
that all elements are pure (that is, capacitors have only capacitance,
inductors only inductance, and resistors only resistance).
Standard counterclockwise vector rotation is used to indicate
angles of lead and lag. A white arrowhead represents
a voltage vector; a black arrowhead is a current
vector. In all cases, the reference is the line along the horizontal,
extending to the right. Relative vectors are shown for all voltages
and currents in each circuit.
Vector-Circuit Quiz Answers
1-B In a series circuit containing only resistance, the current
is in phase with the applied voltage.
2-F In a parallel circuit, there are three currents and a single
voltage, which is used as the reference vector (directed horizontally
to the right). The current in an inductor lags the voltage across
the inductor by 90 degrees. The current into a capacitor leads the
voltage across the capacitor by 90 degrees. The total circuit current
is the difference between the branch currents.
3-J The current is used as the reference vector. The voltage
drops across the capacitor and resistor add vectorially to equal
the applied voltage.
4-H The applied voltage is the reference vector. The current
in the circuit lags the voltage by 90 degrees.
5-G The applied voltage is the reference vector. The two branch
currents add vectorially to equal the circuit current.
6-A The current is used as the reference vector. The voltage
drops across the resistor and inductor add vectorially to equal
the applied voltage.
7-I The current is the reference vector. The voltage drops across
the inductor and capacitor are 180 degrees out of phase, and the
difference between them is equal to the applied voltage.
8-E The applied voltage is the reference. The leading currents
in each branch are in phase and add to equal total circuit current.
9-D The applied voltage is the reference. The two branch currents
add vectorially to equal total circuit current.
10-C The applied voltage is the reference. The current in the
inductor leads the applied voltage by 90 degrees.
Posted June 4, 2014