June 1970 Popular Electronics

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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.

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