#### December 1970 Popular Electronics
[Table
of Contents] People old and young enjoy waxing nostalgic about
and learning some of the history of early electronics. Popular Electronics
was published from October 1954 through April 1985. All copyrights are hereby
acknowledged. See all articles from *
Popular Electronics*. |

Here is a fairly simple quiz on AC circuit analysis. If you
are not already comfortable with adding series and parallel
circuits containing resistors, capacitors, and inductors, you
will appreciate the simple formula presented that will keep
the sweat level down ;-) OK, pick up you pencils... now.

## Quiz on AC Circuit Theory

By Robert P. Balin

Voltage measurements made in a series ac circuit seldom add
up as simply as they do in a dc circuit. You may even find the
voltage across a coil or capacitor to be greater than the supply
voltage! Nevertheless, Ohm's Law and Kirchhoff's Law do apply,
and careful measurements will show that the supply voltage and
the various voltage drops around a series ac circuit are related
in an unusual way: the square of the supply voltage is equal
to the square of the difference between the voltage on the coil
and the voltage on the capacitor, plus the square of the voltage
on the resistor.

This relationship, (V_{Total})^{2} = (V_{L}
- V_{C})^{2} + (V_{R})^{2},can
be used to find any unknown voltage if all others are known.

In parallel ac circuits, the currents add up the same way
as voltages do in a series ac circuit. Brush up on your ac theory
and see if you can solve the missing voltage or current in the
circuits below. Where necessary, the voltages and currents are
related by the 3:4:5 ratio to provide easy, whole number answers.
Only simple algebra is required. Vectors, phasors, and quadratic
equations are not necessary to find the solutions.

(See answers below)

Circuit Quiz Answers

1. (10)^{2}= (8)^{2} + (VR)^{2};
VR = 6V

2. (20)^{2}= (7+VC)^{2}+ (12)^{2};
VC = 9V

3. (24)^{2}= (VL-6)^{2}; VL = 30V

4. (15)^{2}= (350-350)^{2}+ (VR)^{2};
VR = 15V

5. (VT)^{2}= (15-3)^{2}+ (16)^{2};
VT = 20V

6. (50)^{2}= (VL)^{2}+ (12)^{2}=
(VC)^{2}+ (12)2; VL = VC

(VT)^{2}= (VL-VC)^{2}+
(12)^{2}; VT = 12V

7. (IT)^{2}= (6)^{2}+ (8)^{2}; IT
= 10 mA.

8. (20)^{2}= (16-IC)^{2}+ (16)^{2};
IC = 4 mA.

9. (IT)^{2}= (17-13)^{2}+ (3)^{2};
IT = 5 mA.

10. (9)^{2}= (40-4-IC)^{2}; IC = 7 mA.

Posted June 21, 2013