T5 Electrical Principles

D. Amperes

Current is the rate at which electric charge flows past a point in a circuit, and its unit is the ampere (A), often shortened to amp. One ampere is one coulomb of charge passing a point each second.

• A. The volt is the unit of voltage, the electrical pressure that pushes current through a circuit, not the current itself.
• B. The watt is the unit of power, the rate at which energy is used; it equals volts times amperes.
• C. The ohm is the unit of resistance, the opposition to current flow.

B. Watts

Power is the rate at which electrical energy is used or delivered, and its unit is the watt (W). In a DC circuit, power in watts equals voltage times current (P = E x I).

• A. The volt measures voltage, the electrical pressure that drives current, not power.
• C. A watt-hour is a unit of energy (power multiplied by time), such as a battery's stored capacity, not a unit of power.
• D. The ampere measures current, the rate of charge flow, not power.

D. Current

Current is the flow of electric charge through a circuit; in a wire the charge is carried by electrons. It is measured in amperes.

• A. Voltage is the electrical pressure, or potential difference, that causes electrons to flow; it is not the flow itself.
• B. Amperes already express a rate of charge flow (coulombs per second); amperes per second would describe how fast the current is changing.
• C. Volts per second describes how fast a voltage changes, not the flow of electrons.

C. Frequency

Frequency is the number of complete cycles an alternating current makes each second. It is measured in hertz (Hz), where 1 Hz is one cycle per second; US household power, for example, alternates at 60 Hz.

• A. Pulse rate describes how often separate pulses occur in a pulsed signal; it is not the term for the cycles of an alternating current.
• B. Wave number is the number of waves per unit of distance (the inverse of wavelength), not per second.
• D. Wavelength is the distance a wave travels during one cycle, measured in meters, not the number of cycles per second.

A. Voltage

A difference in voltage (potential difference) between two points pushes electrons through a conductor connecting them. With no voltage difference, no current flows, which is why voltage is also called electromotive force.

• B. Ampere-hours measure stored charge, such as a battery's capacity, not the force that makes current flow.
• C. Capacitance is the ability to store energy in an electric field; a difference in capacitance does not drive current.
• D. Inductance is the ability to store energy in a magnetic field and to oppose changes in current; it does not cause electron flow.

A. Hertz

The hertz (Hz) is the unit of frequency, equal to one cycle per second. It replaced the older unit name, cycles per second.

• B. The henry is the unit of inductance, not frequency.
• C. The farad is the unit of capacitance, not frequency.
• D. Epicycles per second is not an electrical unit; the older name for the unit of frequency was cycles per second.

B. They have many free electrons

In a metal, the outer electrons of each atom are loosely held and can move freely through the material. A small voltage moves these free electrons along, so current flows easily.

• A. Density does not determine conductivity; aluminum is much less dense than lead, yet it conducts electricity far better.
• C. Protons are bound in the nuclei of atoms and do not move through a solid conductor; current in a metal is carried by electrons.
• D. Young's modulus measures a material's stiffness under stretching, a mechanical property unrelated to electrical conduction.

B. Glass

An insulator has very few free electrons, so it strongly resists the flow of current. Glass is a good insulator and has long been used to make insulators for power lines and antenna wires.

• A. Sea water contains dissolved salts whose ions carry current, so it conducts fairly well.
• C. Stainless steel is a metal with free electrons; it conducts electricity, though not as well as copper.
• D. Graphite is a form of carbon that conducts electricity; it is used in motor brushes and some resistors.

C. Current that alternates between positive and negative directions

Alternating current (AC) periodically reverses direction, flowing one way (positive) and then the other way (negative) during each cycle. Current that changes in size but never reverses direction is pulsating DC, not AC.

• A. Current that varies between zero and a positive value never reverses, so it is pulsating direct current, not alternating current.
• B. Current that varies between zero and a negative value also flows in only one direction, so it is pulsating direct current.
• D. Only the description with reversal between positive and negative directions fits alternating current; the other two describe current that never changes direction.

C. Power

Power is the rate at which electrical energy is used or delivered, measured in watts. One watt is one joule of energy per second.

• A. Resistance is the opposition to current flow, measured in ohms, not a rate of energy use.
• B. Current is the rate of charge flow, measured in amperes; the rate of energy use also depends on the voltage.
• D. Voltage is the electrical pressure that drives current, measured in volts; it is not a rate of energy use.

D. All these choices are correct

Resistance opposes the flow of any current: direct, alternating, or radio frequency. In each case, current through a resistance turns some electrical energy into heat.

• A. Resistance does oppose direct current, but it opposes AC and RF current too, so this is only part of the answer.
• B. Resistance does oppose alternating current, but it opposes DC and RF current as well, so this is only part of the answer.
• C. Resistance does oppose RF current, which is a form of alternating current, but it also opposes DC and lower-frequency AC, so this is only part of the answer.

C. 1500 milliamperes

The prefix milli means one one-thousandth, so 1 ampere equals 1000 milliamperes. Converting to the smaller unit means multiplying by 1000: 1.5 A x 1000 = 1500 mA.

• A. 0.0000015 mA comes from dividing by 1,000,000 instead of multiplying by 1000; it is a billion times smaller than 1.5 A.
• B. 0.0015 mA comes from dividing by 1000 instead of multiplying; converting to a smaller unit makes the number larger, not smaller.
• D. 1,500,000 mA comes from multiplying by 1,000,000 instead of 1000; it equals 1500 A.

A. 1500 kHz

Kilo means 1000, so divide a frequency in hertz by 1000 to express it in kilohertz: 1,500,000 Hz / 1000 = 1500 kHz. The same frequency is also 1.5 MHz.

• B. 1500 MHz is 1,500,000,000 Hz, a thousand times higher; 1,500,000 Hz is 1.5 MHz.
• C. 15 GHz is 15,000,000,000 Hz, ten thousand times higher than 1,500,000 Hz.
• D. 150 kHz is 150,000 Hz, ten times lower; the decimal point has moved one place too far.

C. One thousand volts

The prefix kilo means one thousand, so one kilovolt (1 kV) equals 1000 volts.

• A. One one-thousandth of a volt is a millivolt (mV); milli and kilo are opposites.
• B. One hundred volts would use the rarely seen prefix hecto; kilo means 1000, not 100.
• D. One million volts is a megavolt (MV); mega means one million.

A. One one-millionth of a volt

The prefix micro (µ) means one one-millionth, so one microvolt (1 µV) is 0.000001 volt. Receiver sensitivity is often stated in microvolts.

• B. One million volts is a megavolt (MV); mega is the opposite of micro.
• C. One thousand kilovolts is 1,000,000 volts (a megavolt), not a tiny fraction of a volt.
• D. One one-thousandth of a volt is a millivolt (mV), which equals 1000 microvolts.

B. 0.5 watts

Milli means one one-thousandth, so divide milliwatts by 1000 to get watts: 500 mW / 1000 = 0.5 W.

• A. 5 watts equals 5000 milliwatts, ten times more than 500 mW.
• C. 500,000 watts comes from multiplying by 1000 instead of dividing; converting to a larger unit makes the number smaller.
• D. 500,000,000 watts comes from multiplying by 1,000,000; it is a billion times more than 0.5 W.

D. 3 amperes

There are 1000 milliamperes in one ampere, so divide by 1000: 3000 mA / 1000 = 3 A.

• A. 0.003 A is 3 mA; it comes from dividing by 1,000,000 instead of 1000.
• B. 0.3 A is 300 mA, ten times less than 3000 mA.
• C. 3,000,000 A comes from multiplying by 1000 instead of dividing; going from milliamperes to amperes makes the number smaller.

C. 3525 kHz

One megahertz equals 1000 kilohertz, so multiply by 1000: 3.525 MHz x 1000 = 3525 kHz.

• A. 0.003525 kHz is 3.525 Hz; it comes from dividing by 1000 instead of multiplying.
• B. 35.25 kHz is 0.03525 MHz, a hundred times lower than 3.525 MHz; the decimal point is in the wrong place.
• D. 3,525,000 kHz is 3525 MHz, a thousand times too high; 3,525,000 is the frequency in hertz, not kilohertz.

B. 1 microfarad

Pico means one trillionth and micro means one millionth, so there are 1,000,000 picofarads in one microfarad. Therefore 1,000,000 pF / 1,000,000 = 1 µF.

• A. 0.001 microfarads equals 1000 picofarads (one nanofarad), a thousand times smaller than 1,000,000 pF.
• C. 1000 microfarads equals 1,000,000,000 picofarads, a thousand times larger than 1,000,000 pF.
• D. 1,000,000,000 microfarads is 1000 farads; it comes from multiplying by a thousand instead of dividing by a million.

B. 3 dB

Decibels compare two power levels: dB = 10 x log(P2 / P1). Going from 5 W to 10 W doubles the power, and 10 x log(10 / 5) = 10 x log(2) = 3.01 dB, about 3 dB. Every doubling of power is an increase of about 3 dB.

• A. 2 dB is a power ratio of about 1.6, which would raise 5 W only to about 7.9 W.
• C. 5 dB is a power ratio of about 3.2, which would raise 5 W to about 16 W.
• D. 10 dB is a tenfold power increase, which would raise 5 W to 50 W.

C. -6 dB

Going from 12 W to 3 W cuts the power to one quarter: 10 x log(3 / 12) = 10 x log(0.25) = -6.02 dB, about -6 dB. Each halving of power is about -3 dB, and 12 W to 6 W to 3 W is two halvings.

• A. -1 dB reduces power to about 79 percent of the original, about 9.5 W from 12 W.
• B. -3 dB reduces power by half, to 6 W from 12 W, not to one quarter.
• D. -9 dB reduces power to about one eighth, roughly 1.5 W from 12 W.

A. 10 dB

Going from 20 W to 200 W is a tenfold power increase: 10 x log(200 / 20) = 10 x log(10) = 10 dB. Every factor of 10 in power adds 10 dB.

• B. 12 dB is a power ratio of about 16, which would raise 20 W to about 317 W.
• C. 18 dB is a power ratio of about 63, which would raise 20 W to about 1260 W.
• D. 28 dB is a power ratio of about 630, which would raise 20 W to about 12,600 W.

D. 28.400 MHz

One megahertz equals 1000 kilohertz, so divide by 1000: 28400 kHz / 1000 = 28.400 MHz. This frequency is in the 10 meter band.

• A. 28.400 kHz is a thousand times lower than 28400 kHz; the decimal point moved without changing the unit.
• B. 2.800 MHz is 2800 kHz, about ten times lower than 28400 kHz, and the digits do not match.
• C. 284.00 MHz is 284,000 kHz, ten times higher than 28400 kHz; the decimal point is one place off.

C. 2.425 GHz

One gigahertz equals 1000 megahertz, so divide by 1000: 2425 MHz / 1000 = 2.425 GHz.

• A. 0.002425 GHz is 2.425 MHz, a thousand times lower; it comes from dividing by 1,000,000 instead of 1000.
• B. 24.25 GHz is 24,250 MHz, ten times higher than 2425 MHz.
• D. 242.5 GHz is 242,500 MHz, a hundred times higher than 2425 MHz.

D. Capacitance

Capacitance is the ability to store energy in an electric field, such as the field between the plates of a capacitor when a voltage is applied across them. It is measured in farads.

• A. Inductance is the ability to store energy in a magnetic field, such as the field around a coil carrying current.
• B. Resistance opposes current and turns electrical energy into heat; it does not store energy.
• C. Frequency is the number of cycles per second of an alternating signal, not an ability to store energy.

A. Farad

The farad (F) is the unit of capacitance. One farad is a large value, so practical capacitors are usually rated in microfarads (µF) or picofarads (pF).

• B. The ohm is the unit of resistance, reactance, and impedance.
• C. The volt is the unit of voltage (electromotive force).
• D. The henry is the unit of inductance, the magnetic counterpart of capacitance.

D. Inductance

Inductance is the ability to store energy in a magnetic field. Current through a coil builds a magnetic field, and the stored energy returns to the circuit when the current decreases. It is measured in henries.

• A. Admittance is the inverse of impedance, a measure of how easily alternating current flows; it is not energy storage.
• B. Capacitance stores energy in an electric field, not a magnetic field.
• C. Resistance converts electrical energy into heat rather than storing it.

C. Henry

The henry (H) is the unit of inductance. Coils used in radio circuits are usually rated in millihenries (mH) or microhenries (µH).

• A. The coulomb is the unit of electric charge.
• B. The farad is the unit of capacitance.
• D. The ohm is the unit of resistance, reactance, and impedance, not inductance.

D. Ohm

Impedance is the total opposition to alternating current, combining resistance and reactance. Like resistance, it is measured in ohms; coaxial feed line, for example, is commonly rated at 50 ohms impedance.

• A. The volt measures voltage, the force that drives current, not the opposition to it.
• B. The ampere measures current, the flow that impedance opposes.
• C. The coulomb measures electric charge.

A. kHz

The prefix kilo is written with a lowercase k, and hertz is written Hz with a capital H because the unit is named after a person, Heinrich Hertz. Together they form kHz.

• B. khz uses a lowercase h; the symbol for hertz is Hz, with a capital H.
• C. KHz uses a capital K; the symbol for the prefix kilo is a lowercase k (capital K is the symbol for the kelvin).
• D. KHZ capitalizes the k and the z; only the H of Hz is a capital letter.

D. MHz

The prefix mega is written with a capital M, and hertz is written Hz, so megahertz is MHz. Case matters: a lowercase m means milli.

• A. mHz means millihertz (one one-thousandth of a hertz), because a lowercase m is the prefix milli.
• B. mHZ uses the milli prefix and also capitalizes the z of Hz.
• C. Mhz uses a lowercase h; the symbol for hertz is Hz.

A. P = I x E

In a DC circuit, power equals current times voltage: P = I x E, with P in watts, I in amperes, and E in volts. For example, 2 A at 12 V delivers 24 W.

• B. Dividing voltage by current gives resistance in ohms (R = E / I), not power.
• C. Squaring the current and multiplying by voltage does not give watts; the related power formula multiplies current squared by resistance (P = I² x R).
• D. Current divided by voltage gives conductance, the inverse of resistance, not power.

A. 138 watts

Power equals voltage times current: P = E x I = 13.8 V x 10 A = 138 W.

• B. 0.7 W comes from dividing the current by the voltage (10 / 13.8 = 0.72), which is not a power formula.
• C. 23.8 W comes from adding the voltage and current (13.8 + 10); power requires multiplying them.
• D. 3.8 W comes from subtracting the current from the voltage (13.8 minus 10), which has no meaning in a power calculation.

B. 30 watts

Power equals voltage times current: P = E x I = 12 V x 2.5 A = 30 W.

• A. 4.8 comes from dividing the voltage by the current (12 / 2.5), which gives resistance in ohms, not power.
• C. 14.5 comes from adding 12 and 2.5; power is the product of voltage and current, not their sum.
• D. 0.208 comes from dividing the current by the voltage (2.5 / 12), which is not power.

B. 10 amperes

Rearrange P = E x I to solve for current: I = P / E = 120 W / 12 V = 10 A.

• A. 0.1 A comes from dividing the voltage by the power (12 / 120), which inverts the formula.
• C. 12 A repeats the voltage value; 12 A at 12 V would deliver 144 W, not 120 W.
• D. 132 comes from adding the power and the voltage (120 + 12), which has no meaning.

A. The opposition to AC current flow

Impedance is the total opposition to alternating current, combining resistance and reactance (the opposition from inductors and capacitors, which changes with frequency). It is measured in ohms.

• B. The inverse of resistance is conductance, a measure of how easily current flows, not the opposition to it.
• C. The inverse of reactance is susceptance; impedance includes reactance rather than inverting it.
• D. Power handling capability is a component rating in watts; impedance is measured in ohms.

B. I = E / R

Ohm's law says voltage equals current times resistance (E = I x R). Dividing both sides by R gives the current: I = E / R. For example, 12 V across 4 ohms drives 3 A.

• A. Multiplying voltage by resistance does not give current; in Ohm's law, current times resistance gives voltage.
• C. Squaring the voltage and multiplying by resistance does not give current or any other standard circuit quantity.
• D. E² / R is the power dissipated in a resistance, measured in watts, not current.

A. E = I x R

Ohm's law states that voltage equals current times resistance: E = I x R, with E in volts, I in amperes, and R in ohms. For example, 2 A through 10 ohms produces 20 V.

• B. Dividing current by resistance does not give voltage; for a given current, a larger resistance needs a larger voltage, so the two multiply.
• C. I² x R is the power dissipated in a resistance, measured in watts, not voltage.
• D. Squaring the current and dividing by resistance does not give voltage or any other standard circuit quantity.

B. R = E / I

Starting from Ohm's law, E = I x R, dividing both sides by I gives the resistance: R = E / I. For example, 12 V driving 4 A means 3 ohms.

• A. E x I is power in watts, not resistance.
• C. Adding volts and amperes has no physical meaning; quantities with different units cannot be added.
• D. Subtracting amperes from volts has no physical meaning; resistance is the ratio of voltage to current.

B. 30 ohms

Use Ohm's law solved for resistance: R = E / I = 90 V / 3 A = 30 ohms.

• A. 3 is the current in amperes, not the resistance; 3 ohms across 90 V would draw 30 A.
• C. 1/30 ohm comes from dividing the current by the voltage (3 / 90), the inverse of the correct formula.
• D. 270 comes from multiplying the voltage by the current (90 x 3), which gives power in watts, not resistance.

C. 8 ohms

Use Ohm's law solved for resistance: R = E / I = 12 V / 1.5 A = 8 ohms.

• A. 18 comes from multiplying 12 by 1.5, which gives power (18 W), not resistance.
• B. 0.125 comes from dividing the current by the voltage (1.5 / 12), the inverse of the correct formula.
• D. 13.5 comes from adding the voltage and the current, which has no meaning in Ohm's law.

A. 3 ohms

Use Ohm's law solved for resistance: R = E / I = 12 V / 4 A = 3 ohms.

• B. 16 comes from adding 12 and 4; Ohm's law divides voltage by current.
• C. 48 comes from multiplying 12 by 4, which gives power (48 W), not resistance.
• D. 8 comes from subtracting 4 from 12, which has no meaning in Ohm's law.

D. 1.5 amperes

Use Ohm's law solved for current: I = E / R = 120 V / 80 ohms = 1.5 A.

• A. 9600 comes from multiplying the voltage by the resistance (120 x 80), which does not give current.
• B. 200 comes from adding 120 and 80; Ohm's law divides voltage by resistance.
• C. 0.667 comes from dividing the resistance by the voltage (80 / 120), the inverse of the correct formula.

C. 2 amperes

Use Ohm's law solved for current: I = E / R = 200 V / 100 ohms = 2 A.

• A. 20,000 comes from multiplying the voltage by the resistance (200 x 100), which does not give current.
• B. 0.5 comes from dividing the resistance by the voltage (100 / 200), the inverse of the correct formula.
• D. 100 A repeats the resistance value; 100 A through 100 ohms would take 10,000 V.

C. 10 amperes

Use Ohm's law solved for current: I = E / R = 240 V / 24 ohms = 10 A.

• A. 2400 A is far too large; at 240 V it would require a resistance of only 0.1 ohm.
• B. 0.1 comes from dividing the resistance by the voltage (24 / 240), the inverse of the correct formula.
• D. 5760 comes from multiplying the voltage by the resistance (240 x 24), which does not give current.

A. 1 volt

Use Ohm's law: E = I x R = 0.5 A x 2 ohms = 1 V.

• B. 0.25 comes from dividing the current by the resistance (0.5 / 2); Ohm's law multiplies them.
• C. 2.5 comes from adding 2 and 0.5; voltage is the product of current and resistance, not their sum.
• D. 1.5 comes from subtracting 0.5 from 2, which has no meaning in Ohm's law.

B. 10 volts

Use Ohm's law: E = I x R = 1 A x 10 ohms = 10 V.

• A. 1 V repeats the current value instead of multiplying; 1 V across 10 ohms would drive only 0.1 A.
• C. 11 comes from adding the current and the resistance (1 + 10); Ohm's law multiplies them.
• D. 9 comes from subtracting the current from the resistance (10 minus 1), which has no meaning in Ohm's law.

D. 20 volts

Use Ohm's law: E = I x R = 2 A x 10 ohms = 20 V.

• A. 8 comes from subtracting 2 from 10, which has no meaning in Ohm's law.
• B. 0.2 comes from dividing the current by the resistance (2 / 10); Ohm's law multiplies them.
• C. 12 comes from adding 2 and 10; voltage is the product of current and resistance, not their sum.

A. Series

In a series circuit, components are connected end to end in a single path, so the same current passes through every component. The voltage divides among the components in proportion to their resistance.

• B. In a parallel circuit, every component has the same voltage across it, but the current divides among the branches.
• C. Resonant describes a circuit tuned to one frequency by an inductor and a capacitor; a resonant circuit can be series or parallel, so the term says nothing about equal current.
• D. A branch is one path of a parallel circuit; the total current divides among the branches, so it is not the same in each.

B. Parallel

In a parallel circuit, every component connects across the same two points, so each one has the same voltage across it. The current divides among the branches according to their resistance.

• A. In a series circuit, the current is the same through all components, but the voltage divides among them.
• C. Resonant describes a circuit tuned to one frequency by an inductor and a capacitor; it can be series or parallel, so the term does not guarantee equal voltages.
• D. Branch names one path within a parallel circuit, not a type of circuit; components in series within a single branch can have different voltages.