or
Subelement B
Electrical Math
Section 18
Calculations
What is the magnitude of the impedance of a series AC circuit having a resistance of 6 ohms, an inductive reactance of 17 ohms, and zero capacitive reactance?
• 6.6 ohms.
• 11 ohms.
18 ohms.
• 23 ohms.

What is the magnitude of the impedance of a series AC circuit having a resistance of
6 ohms, an inductive reactance of
17 ohms, and
zero capacitive reactance?

18 ohms.

From wp2ahg:

\begin{align} Z &= \sqrt{(R^2 + (XL- XC)^2)}\\ &= \sqrt{(6^2\text{ ohms} + (17\text{ ohms} - 0\text{ ohms})^2)}\\ &=\sqrt{(36\text{ ohms} + 289\text{ ohms}}\\ &=\sqrt{(325\text{ ohms}}\\ &= 18.02\text{ ohms}\\ \\ \end{align}

Where
Z = Magnitude of Impedance,
R = circuit resistance,
XL = inductive reactance,
XC = capacitive reactance

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A 1-watt, 10-volt Zener diode with the following characteristics: Imin. = 5 mA; Imax. = 95 mA; and Z = 8 ohms, is to be used as part of a voltage regulator in a 20-V power supply. Approximately what size current-limiting resistor would be used to set its bias to the midpoint of its operating range?
• 100 ohms.
200 ohms.
• 1 kilohms.
• 2 kilohms.

A 1-watt, 10-volt Zener diode with the following characteristics:
Imin. = 5 mA;
Imax. = 95 mA; and
Z = 8 ohms,
is to be used as part of a voltage regulator in a 20-V power supply.

Approximately what size current-limiting resistor would be used to set its bias to the midpoint of its operating range?

200 ohms.

From kd7bbc:

https://www.electronics-tutorials.ws/diode/diode_7.html

The zener voltage regulator consists of a current limiting resistor RS connected in series with the input voltage VS with the zener diode connected in parallel with the load RL in this reverse biased condition. The stabilized output voltage is always selected to be the same as the breakdown voltage $V_Z$ of the diode.

$R_S = \frac{(V_S - V_Z)}{IZ}$

In this example: $V_S = 20 V$ $V_Z = 10 V$

For the midpoint of its operating range: $I_Z = \frac{(5 \text{mA} + 95 \text{mA})}{2} = 50 \text{mA}$

Therefore, $R_S = \text{200 ohms}$

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Given a power supply with a no load voltage of 12 volts and a full load voltage of 10 volts, what is the percentage of voltage regulation?
• 17 %
• 80 %
20 %
• 83 %

Given a power supply with a no load voltage of
12 volts and a full load voltage of
10 volts,
what is the percentage of voltage regulation?

20 %

From haihuynh8108:

% Volt Reg = [(Vnl − Vfl) ÷ Vfl ] ∗ 100%

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What turns ratio does a transformer need in order to match a source impedance of 500 ohms to a load of 10 ohms?
7.1 to 1.
• 14.2 to 1.
• 50 to 1.
• None of these.

What turns ratio does a transformer need in order to match a source impedance of 500 ohms to a load of 10 ohms?

7.1 to 1.

From kd7bbc:

The transformer turns ratio is proportional to the Square Root of the Impedance Ratio.

\begin{align} \text{Impedance Ratio} &= 50 : 1\\ \\ \text{Turns Ratio} &= \sqrt{50}:\sqrt{1}\\ &= 7.07:1\ \end{align}

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Given a power supply with a full load voltage of 200 volts and a regulation of 25%, what is the no load voltage?
• 150 volts.
• 160 volts.
• 240 volts.
250 volts.

Given a power supply with a full load voltage of 200 volts and a regulation of 25%, what is the no load voltage?

250 volts.

From wp2ahg:

No Load Vols = (200 volts ∗ 25%) +200 volts
No Load Vols = 50 volts + 200 volts
No Load Vols = 250 volts

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What is the conductance (G) of a circuit if 6 amperes of current flows when 12 volts DC is applied?
• 0.25 Siemens (mhos).
0.50 Siemens (mhos).
• 1.00 Siemens (mhos).
• 1.25 Siemens (mhos).

What is the conductance (G) of a circuit if 6 amperes of current flows when 12 volts DC is applied?

0.50 Siemens (mhos).

From wp2ahg.:

Conductance (G) is the inverse of resistance.

You can see this in the unit of measure commonly used--'mho' is 'ohm' backwards.

(Siemens are also used as a unit of measure for conductance).

So, you can use Ohm's Law to calculate the conductance by solving for resistance, but solve for the inverse instead.

RESISTANCE
R = E ÷ I is normally used for calculating ohms .

CONDUCTANCE
G = I ÷ E can be used for calculating mhos.

G = 6 amps ÷ 12 volts
G = 0.5 mhos (Siemens)

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