Question 1

A motor takes a current of 27.5 amperes per leaf on a 440-volt, three-phase circuit. The power factor is 0.80. What is the load in watts? Round the answer to the nearer whole watt. For a three-phase circuit: $I _ { S }$

Accepted Answer

16766

Question 2

Find the impedance of a coil with 5.5 ohms resistance and 8.2 ohms reactance. Round the answer to the nearer hundredth.

Accepted Answer

9.87

Question 3

The temperature of a motor rises to $E _ { C }$ C above room temperature. The room temperature is $E_ b$ C. What will a Fahrenheit thermometer read? Carry the answer to one decimal place. $E _ { a }$

Accepted Answer

168.8

Question 4

If a 25-horsepower motor takes 96 amperes at full load, and the motor efficiency is 90%, what is the terminal voltage? Express the answer to the nearer hundredth. $E _ { 1 }$

Accepted Answer

The answer of If a 25-horsepower motor takes 96 amperes...

Question 5

If $E _ { a }$ is the unknown resistance of the Wheatstone bridge arrangement shown in the figure, find the value of this unknown resistance. Carry the answer to one decimal place. $E_ b$

Accepted Answer

The answer of If $E _ { a }$ is...

Question 6

The total capacitance ( C ) is directly proportional to the product of the dielectric constant ( k ) and plate area ( A ) and inversely proportional to the thickness ( d ) of the dielectric.
A) $C = \frac { k d } { A }$
B) $C = \frac { k A } { d }$
C) $C = \frac { k } { d A }$
D) $C = \frac { d } { k A }$

Accepted Answer

The equation for the total capacitance (C) is C = (kA)/d where k is the dielectric constant, A is the plate area, and d is the thickness of the dielectric. This equation shows the proportionality of C to kA and the inverse proportionality of C to d. Therefore, choice B is the correct equation.

Question 7

In a circuit, what current does a 220-volt, 5-horsepower motor receive if the efficiency of the motor is 80%? Express the answer to the nearer hundredth. $$\theta = 360 t _ { i } f$$

Accepted Answer

The answer of In a circuit, what current does a...

Question 8

Find the power used in the single-phase circuit shown. Carry the answer to three decimal places. $X _ { L }$

Accepted Answer

The answer of Find the power used in the single-phase...

Question 9

The resonant frequency ( $f _ { r }$ ) of a circuit containing both inductance ( L ) and capacitance ( C ) may be found by the reciprocal of two pi ( $2 \pi$ ) Hint:((The reciprocal is 1/$2 \pi$ )) multiplied by the square root of the product of the inductance and capacitance.
A) $f _ { r } = \sqrt { L C } / 2 \pi$
B) $f _ { r } = 1 / 2 \pi \sqrt { L C }$
C) $f _ { r } = L / 2 \pi \sqrt { L C }$
D) $f _ { r } = C / 2 \pi \sqrt { L C }$

Accepted Answer

The formula for resonant frequency is $f _ { r } = 1 / 2 \pi \sqrt { L C }$ as given in the prompt.

Question 10

A three-phase, three-wire circuit delivers 175 amperes at a voltage of 220 volts with a 0.85 power factor. What is the kilowatt load to the nearer hundredth? 
$\begin{array}{llcc}
\text {k W load }= \frac { \sqrt { 3 } ( E ) ( D ) ( P F ) } { 1,000 } &\text {  where k W load = 3-phase power in kilowatts}\
&\text {i =  current in amperes}\
&\text {X = voltage involts}\
&\text {P F = power factor}\
\end{array}$

Accepted Answer

The answer of A three-phase, three-wire circuit delivers 175 amperes...

Question 11

The current ( I ) in an electrical circuit is directly proportional to the voltage applied ( E ) and inversely proportional to the circuit impedance.
A) $I = \frac { Z } { E }$
B) $E = \frac { V } { I }$
C) $I = \frac { E } { Z }$
D) $I = \frac { E ^ { 2 } } { Z }$

Accepted Answer

This follows Ohm's law, which states that I = V/Z, where V is the voltage and Z is the impedance. By manipulating the equation, we can get I = E/Z. Therefore, option C is the best choice.

Question 12

The internal resistance of five cells is 1.8 ohms each. The cells are connected as shown in the diagram to a 2-ohm resistance. What current, to the nearer hundredth, exists in the circuit? $E_ X$

Accepted Answer

The answer of The internal resistance of five cells is...

Question 13

An electrical motor has a degree of efficiency ( Eff ) equal to the ratio of its useful output power ( $P _ { 0 }$ ) to the input power ( $p _ { 1 }$ ) required to operate it.
A) $E f f = \frac { P _ { 0 } } { P _ { 1 } }$
B) $E f f = \frac { P _ { 1 } } { P _ { 2 } }$
C) $E f f = \frac { P ^ { 2 } 0 } { P _ { 1 } }$
D) $E f f = \frac { P _ { 1 } } { P _ { 0 } }$

Accepted Answer

The efficiency of an electrical motor is defined as the ratio of its useful output power to the input power required to operate it. Therefore, option A is the correct formula for efficiency. Option B is incorrect because it does not take into account the useful output power. Option C is also incorrect because raising the output power to the power of 2 would not lead to an accurate measure of efficiency. Option D is incorrect because it has the useful output power in the denominator, which is not the correct placement for this term in the efficiency formula.

Question 14

A motor takes 38 amperes on a 220-volt circuit. Find the horsepower output (hp) of the motor shown with an efficiency of 90%. Express the answer to the nearest hundredth. $$X _ { L }$$

Accepted Answer

The answer of A motor takes 38 amperes on a...

Question 15

What is the resistance of $E _ { \text {LINE } }$ if the total resistance $E_ X$ of the parallel circuit shown is 3.2 ohms? $E _R$

Accepted Answer

The answer of What is the resistance of \(E _...

Question 16

The electrostatic force ( F ) between two plates of a charged capacitor is directly proportional to the product of the charges ( $q_ 1$ and $q_2$ ) on each plate and inversely proportional to the square of the distance ( d ) between the plates.
A) $F = \frac { q _ { 1 } } { d q _ { 2 } }$
B) $F = \frac { d } { q 1 q 2 }$
C) $F = \frac { q 1 q 2 } { d }$
D) $F = \frac { q 1 q 2 } { d ^ { 2 } }$

Accepted Answer

According to the statement of the problem, the electrostatic force (F) is directly proportional to the product of the charges (q1 and q2) and inversely proportional to the square of the distance (d) between the plates. The exact mathematical relationship can be written as:

F ∝ (q1q2)/d^2

where the symbol ∝ means "is proportional to". To remove the proportionality sign and obtain an exact equality, we need to introduce a proportionality constant, which is usually denoted by k:

F = k(q1q2)/d^2

The value of the constant k depends on the units used to measure F, q1, q2, and d, as well as on the properties of the medium between the plates (e.g. the permittivity of free space). However, we don't need to know the exact value of k to answer the question. We just need to find the expression that correctly represents the relationship between F, q1, q2, and d. By comparing the given options with the above equation, we can identify that only option D matches:

F = (q1q2)/d^2

Therefore, the answer is D, and the explanation is as above.

Question 17

Determine the horsepower output to the nearer hundredth for the motor in the circuit shown.

Accepted Answer

The answer of Determine the horsepower output to the nearer...

Question 18

If a current of 4.5 amperes exists, what is the impedance of a circuit having a voltage of 110 volts across it? Express the answer to the nearer hundredth. $$\begin{aligned}
Z = \frac { E } { I } \quad \text { where } & Z = \text { impedance in ohms } \
& E = \text { voltage in volts } \
I & = \text { current in amperes }
\end{aligned}$$

Accepted Answer

The answer of If a current of 4.5 amperes exists,...

Question 19

Solve the equation for the current ( I ) required by a motor when the horsepower, percent efficiency of the motor, and the voltage are known. $$\begin{aligned}
h p = \frac { ( E ) ( I ) ( E f f ) } { 746 } \quad \text { where } & l = \text { current in amperes } \
& E = \text { voltage in volts } \
& E f f = \text { efficiency of motor } \
& h p = \text { horsepower }
\end{aligned}$$
A) $I = \frac { 746 } { E \times E f f \times h p }$
B) $I = \frac { 746 ( h p ) } { E \times E f f }$
C) $I = \frac { ( h p ) } { 746 E \times E f f }$
D) $I = \frac { E \times E f f } { 746 ( h p ) }$

Accepted Answer

If we solve the given equation for I, we get:
$$I=\frac{746\cdot hp}{E\cdot Eff}$$
So, the correct option is B.

Question 20

Find the resistance of 240 feet of number 10 copper wire with a cross-sectional area ( $X _ { L } = \sqrt { Z ^ { 2 } - R ^ { 2 } }$ ) of 10,380 circular mils. Express the answer to the nearer hundredth.

Accepted Answer

The answer of Find the resistance of 240 feet of...

Quiz 8: Formulas

A motor takes a current of 27.5 amperes per leaf on a 440-volt, three-phase circuit. The power factor is 0.80. What is the load in watts? Round the answer to the nearer whole watt. For a three-phase circuit: $I _ { S }$

Find the impedance of a coil with 5.5 ohms resistance and 8.2 ohms reactance. Round the answer to the nearer hundredth.

The temperature of a motor rises to $E _ { C }$ C above room temperature. The room temperature is $E_ b$ C. What will a Fahrenheit thermometer read? Carry the answer to one decimal place. $E _ { a }$

If a 25-horsepower motor takes 96 amperes at full load, and the motor efficiency is 90%, what is the terminal voltage? Express the answer to the nearer hundredth. $E _ { 1 }$

If $E _ { a }$ is the unknown resistance of the Wheatstone bridge arrangement shown in the figure, find the value of this unknown resistance. Carry the answer to one decimal place. $E_ b$

The total capacitance ( C ) is directly proportional to the product of the dielectric constant ( k ) and plate area ( A ) and inversely proportional to the thickness ( d ) of the dielectric.

In a circuit, what current does a 220-volt, 5-horsepower motor receive if the efficiency of the motor is 80%? Express the answer to the nearer hundredth. $\theta = 360 t _ { i } f$

Find the power used in the single-phase circuit shown. Carry the answer to three decimal places. $X _ { L }$

The resonant frequency ( $f _ { r }$ ) of a circuit containing both inductance ( L ) and capacitance ( C ) may be found by the reciprocal of two pi ( $2 \pi$ ) Hint:((The reciprocal is 1/ $2 \pi$ ) ) multiplied by the square root of the product of the inductance and capacitance.

The current ( I ) in an electrical circuit is directly proportional to the voltage applied ( E ) and inversely proportional to the circuit impedance.

The internal resistance of five cells is 1.8 ohms each. The cells are connected as shown in the diagram to a 2-ohm resistance. What current, to the nearer hundredth, exists in the circuit? $E_ X$

An electrical motor has a degree of efficiency ( Eff ) equal to the ratio of its useful output power ( $P _ { 0 }$ ) to the input power ( $p _ { 1 }$ ) required to operate it.

A motor takes 38 amperes on a 220-volt circuit. Find the horsepower output (hp) of the motor shown with an efficiency of 90%. Express the answer to the nearest hundredth. $X _ { L }$

What is the resistance of $E _ { \text {LINE } }$ if the total resistance $E_ X$ of the parallel circuit shown is 3.2 ohms? $E _R$

The electrostatic force ( F ) between two plates of a charged capacitor is directly proportional to the product of the charges ( $q_ 1$ and $q_2$ ) on each plate and inversely proportional to the square of the distance ( d ) between the plates.

Determine the horsepower output to the nearer hundredth for the motor in the circuit shown.

Quiz 8: Formulas

A motor takes a current of 27.5 amperes per leaf on a 440-volt, three-phase circuit. The power factor is 0.80. What is the load in watts? Round the answer to the nearer whole watt. For a three-phase circuit: ISI _ { S }IS​

Find the impedance of a coil with 5.5 ohms resistance and 8.2 ohms reactance. Round the answer to the nearer hundredth.

The temperature of a motor rises to ECE _ { C }EC​ C above room temperature. The room temperature is EbE_ bEb​ C. What will a Fahrenheit thermometer read? Carry the answer to one decimal place. EaE _ { a }Ea​

If a 25-horsepower motor takes 96 amperes at full load, and the motor efficiency is 90%, what is the terminal voltage? Express the answer to the nearer hundredth. E1E _ { 1 }E1​

If EaE _ { a }Ea​ is the unknown resistance of the Wheatstone bridge arrangement shown in the figure, find the value of this unknown resistance. Carry the answer to one decimal place. EbE_ bEb​

The total capacitance ( C ) is directly proportional to the product of the dielectric constant ( k ) and plate area ( A ) and inversely proportional to the thickness ( d ) of the dielectric.

In a circuit, what current does a 220-volt, 5-horsepower motor receive if the efficiency of the motor is 80%? Express the answer to the nearer hundredth. θ=360tif\theta = 360 t _ { i } fθ=360ti​f

Find the power used in the single-phase circuit shown. Carry the answer to three decimal places. XLX _ { L }XL​

The resonant frequency ( frf _ { r }fr​ ) of a circuit containing both inductance ( L ) and capacitance ( C ) may be found by the reciprocal of two pi ( 2π2 \pi2π ) Hint:((The reciprocal is 1/ 2π2 \pi2π ) ) multiplied by the square root of the product of the inductance and capacitance.

The current ( I ) in an electrical circuit is directly proportional to the voltage applied ( E ) and inversely proportional to the circuit impedance.

The internal resistance of five cells is 1.8 ohms each. The cells are connected as shown in the diagram to a 2-ohm resistance. What current, to the nearer hundredth, exists in the circuit? EXE_ XEX​

An electrical motor has a degree of efficiency ( Eff ) equal to the ratio of its useful output power ( P0P _ { 0 }P0​ ) to the input power ( p1p _ { 1 }p1​ ) required to operate it.

A motor takes 38 amperes on a 220-volt circuit. Find the horsepower output (hp) of the motor shown with an efficiency of 90%. Express the answer to the nearest hundredth. XLX _ { L }XL​

What is the resistance of ELINE E _ { \text {LINE } }ELINE ​ if the total resistance EXE_ XEX​ of the parallel circuit shown is 3.2 ohms? ERE _RER​

The electrostatic force ( F ) between two plates of a charged capacitor is directly proportional to the product of the charges ( q1q_ 1q1​ and q2q_2q2​ ) on each plate and inversely proportional to the square of the distance ( d ) between the plates.

Determine the horsepower output to the nearer hundredth for the motor in the circuit shown.

Find the resistance of 240 feet of number 10 copper wire with a cross-sectional area ( XL=Z2−R2X _ { L } = \sqrt { Z ^ { 2 } - R ^ { 2 } }XL​=Z2−R2​ ) of 10,380 circular mils. Express the answer to the nearer hundredth.

A motor takes a current of 27.5 amperes per leaf on a 440-volt, three-phase circuit. The power factor is 0.80. What is the load in watts? Round the answer to the nearer whole watt. For a three-phase circuit: $I _ { S }$

The temperature of a motor rises to $E _ { C }$ C above room temperature. The room temperature is $E_ b$ C. What will a Fahrenheit thermometer read? Carry the answer to one decimal place. $E _ { a }$

If a 25-horsepower motor takes 96 amperes at full load, and the motor efficiency is 90%, what is the terminal voltage? Express the answer to the nearer hundredth. $E _ { 1 }$

If $E _ { a }$ is the unknown resistance of the Wheatstone bridge arrangement shown in the figure, find the value of this unknown resistance. Carry the answer to one decimal place. $E_ b$

In a circuit, what current does a 220-volt, 5-horsepower motor receive if the efficiency of the motor is 80%? Express the answer to the nearer hundredth. $\theta = 360 t _ { i } f$

Find the power used in the single-phase circuit shown. Carry the answer to three decimal places. $X _ { L }$

The resonant frequency ( $f _ { r }$ ) of a circuit containing both inductance ( L ) and capacitance ( C ) may be found by the reciprocal of two pi ( $2 \pi$ ) Hint:((The reciprocal is 1/ $2 \pi$ ) ) multiplied by the square root of the product of the inductance and capacitance.

The internal resistance of five cells is 1.8 ohms each. The cells are connected as shown in the diagram to a 2-ohm resistance. What current, to the nearer hundredth, exists in the circuit? $E_ X$

An electrical motor has a degree of efficiency ( Eff ) equal to the ratio of its useful output power ( $P _ { 0 }$ ) to the input power ( $p _ { 1 }$ ) required to operate it.

A motor takes 38 amperes on a 220-volt circuit. Find the horsepower output (hp) of the motor shown with an efficiency of 90%. Express the answer to the nearest hundredth. $X _ { L }$

What is the resistance of $E _ { \text {LINE } }$ if the total resistance $E_ X$ of the parallel circuit shown is 3.2 ohms? $E _R$

The electrostatic force ( F ) between two plates of a charged capacitor is directly proportional to the product of the charges ( $q_ 1$ and $q_2$ ) on each plate and inversely proportional to the square of the distance ( d ) between the plates.