Question 1

You need an ideal transformer to reduce a voltage of 150 V in the primary circuit to 25 V in the secondary circuit.The primary circuit has 130 windings and the secondary circuit is completed through a 55-Ω resistor.How many windings should the secondary circuit contain?

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Question 2

An ac generator contains 80 flat rectangular loops of wire,each of which is 12 cm long and 8 cm wide.The loops rotate at 1200 rpm about an axis through the center and parallel to the long side.If the $\vec { B }$ field in which the loop rotates is uniform,has magnitude 0.30 T,and is perpendicular to the axis of rotation,what will be the maximum output voltage of this generator?

Accepted Answer

The maximum output voltage of an AC generator is given by:$$V_{max} = NBl\omega$$where:* N is the number of loops* B is the magnetic field strength* l is the length of each loop* \omega is the angular velocityIn this problem, we have:* N = 80* B = 0.30 T* l = 12 cm = 0.12 m* \omega = 1200 rpm = 125.66 rad/sPlugging these values into the equation, we get:$$V_{max} = (80)(0.30 T)(0.12 m)(125.66 rad/s) = 29 V$$Therefore, the maximum output voltage of this generator is 29 V.

Question 3

An ideal step-down transformer is needed to reduce a primary voltage of 120 V to 6.0 V.What must be the ratio of the number of turns in the secondary to the number of turns in the primary?

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Question 4

A generator produces 60 A of current at 120 V.The voltage is usually stepped up to 4500 V by an ideal transformer and transmitted through a power line of total resistance 1.0 Ω.Find the number of turns in the secondary if the primary has 200 turns.

Accepted Answer

The number of turns in the secondary can be found using the transformer equation, which relates the primary and secondary voltages and the number of turns in the primary and secondary coils: $V_p/V_s = N_p/N_s$. Given $V_p = 120V$, $V_s = 4500V$, and $N_p = 200$, solving for $N_s$ gives $N_s = (V_s/V_p) * N_p = (4500/120) * 200 = 7500$.

Question 5

An ac generator with a total resistance of 12 Ω contains 100 flat loops of wire,each with an area of 0.090 m².The loops rotate at 60 rev/s in a $\vec { B }$ field of magnitude 0.50 T.What is the maximum possible induced current?

Accepted Answer

The maximum possible induced current can be found using the formula:

\begin{align*}
I_{max}&=\frac{\omega B A N}{R}\
&=\frac{2 \pi f B A N}{R}
\end{align*}

where $\omega$ is the angular velocity, $f$ is the frequency, $B$ is the magnetic field strength, $A$ is the area of each loop, $N$ is the number of loops, and $R$ is the total resistance.

Substituting the given values:

\begin{align*}
I_{max}&=\frac{2 \pi (60	ext{ rev/s}) (0.50	ext{ T}) (0.090	ext{ m}^2) (100)}{12	ext{ }\Omega}\
&= 0.14	ext{ kA}
\end{align*}

Therefore, the answer is choice C.

Question 6

A circular coil with 600 turns has a radius of 15 cm.The coil is rotating about an axis perpendicular to a magnetic field $\vec { B }$ of 0.020 T in magnitude.If the maximum induced emf in the coil is 1.6 V,at what angular frequency is the coil rotating?

Accepted Answer

The maximum induced emf ($ \epsilon $) in a rotating coil is given by $ \epsilon = NAB\omega $, where $ N $ is the number of turns, $ A $ is the area of the coil, $ B $ is the magnetic field, and $ \omega $ is the angular frequency. Solving for $ \omega $, we have $ \omega = \frac{\epsilon}{NAB} $. Substituting the given values: $ \epsilon = 1.6 \, \text{V} $, $ N = 600 $, $ B = 0.020 \, \text{T} $, and $ A = \pi (0.15)^2 $, we find $ \omega \approx 1.9 \, \text{rad/s} $.

Question 7

A conducting rod whose length is ℓ = 1.60 m is placed on frictionless U-shaped metal rails that is connected to a lightbulb having a resistance of 4.00 Ω as shown in the figure.The rails and the rod are in the plane of the page.A constant uniform $\vec { B }$ field 2.20 T in magnitude is applied perpendicular to and out of the paper.An external force exerted on the rod moves the rod to the right with a constant speed of 6.00 m/s.At what rate is electric energy converted into internal energy in the lightbulb?

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Question 8

An ac generator consists of 100 loops of wire,each of area 0.090 m²,and has a total resistance 12 Ω.The loops rotate about a diameter in a magnetic field of 0.50 T at a constant angular speed of 60 revolutions per second.Find the maximum induced emf in the generator.

Accepted Answer

The maximum induced emf in the generator can be calculated using the formula:

Emax = NABω

where N is the number of loops, A is the area of each loop, B is the magnetic field strength, and ω is the angular speed.

Substituting the given values, we get:

Emax = (100)(0.090 m²)(0.50 T)(2π(60 rev/s))

Emax = 1.7 kV

Therefore, the correct choice is C, with a maximum induced emf of 1.7 kV.

Question 9

In an ideal transformer,how many turns are necessary in a 110-V primary if the 24-V secondary has 100 turns?

Accepted Answer

The turns ratio in a transformer is directly proportional to the voltage ratio. Therefore, if the secondary has 100 turns and produces 24 V, for a primary voltage of 110 V, the number of turns in the primary would be calculated as follows: (110 V / 24 V) * 100 turns = 458.33 turns. Since we're dealing with ideal conditions and whole numbers of turns, rounding to the nearest whole number gives 458 turns.

Question 10

An ideal step-up transformer doubles a primary voltage of 110 V.What is the ratio of the number of turns in its primary coil to the number of turns in the secondary coil?

Accepted Answer

A step-up transformer increases voltage, so if it doubles the voltage from 110 V to 220 V, the ratio of the primary to secondary turns must be 1:2, meaning for every turn in the primary, there are two turns in the secondary.

Question 11

You are designing an ac generator with a maximum emf of 8.0 V.If the generator coil has 200 turns,each with a cross-sectional area of 0.030 m²,what should be the frequency of the generator in a magnetic field of 0.030 T?

Accepted Answer

The maximum emf (E_max) generated by an AC generator can be calculated using the formula: E_max = NABω, where N is the number of turns, A is the area of the coil, B is the magnetic field strength, and ω is the angular frequency (ω = 2πf, where f is the frequency in Hz). Rearranging the formula to solve for f gives: f = E_max / (2πNAB). Substituting the given values: f = 8.0 / (2π * 200 * 0.030 * 0.030) = 7.1 Hz.

Question 12

You wish to construct a simple ac generator with a maximum output of 12 V when rotated at 60 Hz.A magnetic field of 0.050 T is available.If the area of the rotating coil is 100 cm²,how many turns are needed?

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Question 13

A conducting rod whose length is ℓ = 25 cm is placed on a U-shaped metal wire that is connected to a lightbulb having a resistance of 8.0 Ω as shown in the figure.The wire and the rod are in the plane of the page.A constant uniform $\vec { B }$ field of 0.40 T in magnitude is applied perpendicular to and out of the paper.An external applied force moves the rod to the left with a constant speed of 12 m/s.What are the magnitude and direction of the induced current in the circuit?

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Question 14

A conducting rod whose length is ℓ = 1.60 m is placed on frictionless U-shaped metal rails that is connected to a lightbulb having a resistance of 4.00 Ω as shown in the figure.The rails and the rod are in the plane of the page.A constant uniform $\vec { B }$ field of 2.20 T in magnitude is applied perpendicular to and out of the paper.What is the magnitude of the external force needed to move the rod to the right with a constant speed of 6.00 m/s?

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Question 15

The coil of an ac generator has 50 loops and a cross-sectional area of 0.25 m².What is the maximum emf that can be generated by this generator if it is spinning with an angular speed of 4.0 rad/s in a 2.0-T $\vec { B }$ field?

Accepted Answer

The maximum emf ($ \varepsilon_{max} $) generated by an AC generator can be calculated using the formula: $ \varepsilon_{max} = NBA\omega $, where $N$ is the number of loops, $B$ is the magnetic field strength, $A$ is the cross-sectional area of the coil, and $\omega$ is the angular speed. Substituting the given values: $ \varepsilon_{max} = 50 \times 2.0 \times 0.25 \times 4.0 = 100 $ V.

Question 16

The primary of an ideal transformer has 100 turns and its secondary has 200 turns.If the input voltage to the primary is 100 V,we can expect the output voltage of the secondary to be

Accepted Answer

The output voltage of an ideal transformer can be calculated using the formula V2/V1 = N2/N1, where V1 is the input voltage, V2 is the output voltage, N1 is the number of turns in the primary coil, and N2 is the number of turns in the secondary coil. Plugging in the values given, we get V2/100V = 200/100, or V2 = 200V. Therefore, the output voltage of the secondary is 200 V.

Question 17

A rectangular coil of N turns,length L = 25 cm,and width w = 15 cm,as shown in the figure,is rotating in a magnetic field of 1.6 T with a frequency of 75 Hz.If the coil develops a maximum emf 56.9 V,what is the value of N?

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Question 18

The primary coil of an ideal transformer has 100 turns and its secondary coil has 400 turns.If the ac voltage applied to the primary coil is 120 V,what voltage is present in its secondary coil?

Accepted Answer

The voltage ratio of an ideal transformer is equal to the turns ratio. So in this case, the voltage in the secondary coil is 4 times the voltage in the primary coil. Therefore, the voltage in the secondary coil is 4 x 120 V = 480 V.

Question 19

A conducting rod whose length is ℓ = 27.0 cm is placed on frictionless U-shaped metal rails that is connected to a lightbulb having a resistance of 5.00 Ω as shown in the figure.The rails and the rod are in the plane of the page.A constant $\vec { B }$ magnetic field 1.20 T in magnitude is applied perpendicular to and out of the paper.An external force exerted on the rod moves the rod to the right with a constant speed.At what speed should the rod be pulled so that the lightbulb will consume energy at a rate of 1.10 W?

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Quiz 19: Electromagnetic Induction

You need an ideal transformer to reduce a voltage of 150 V in the primary circuit to 25 V in the secondary circuit.The primary circuit has 130 windings and the secondary circuit is completed through a 55-Ω resistor.How many windings should the secondary circuit contain?

An ideal step-down transformer is needed to reduce a primary voltage of 120 V to 6.0 V.What must be the ratio of the number of turns in the secondary to the number of turns in the primary?

A generator produces 60 A of current at 120 V.The voltage is usually stepped up to 4500 V by an ideal transformer and transmitted through a power line of total resistance 1.0 Ω.Find the number of turns in the secondary if the primary has 200 turns.

An ac generator with a total resistance of 12 Ω contains 100 flat loops of wire,each with an area of 0.090 m2.The loops rotate at 60 rev/s in a B⃗\vec { B }B field of magnitude 0.50 T.What is the maximum possible induced current?

A circular coil with 600 turns has a radius of 15 cm.The coil is rotating about an axis perpendicular to a magnetic field B⃗\vec { B }B of 0.020 T in magnitude.If the maximum induced emf in the coil is 1.6 V,at what angular frequency is the coil rotating?

An ac generator consists of 100 loops of wire,each of area 0.090 m2,and has a total resistance 12 Ω.The loops rotate about a diameter in a magnetic field of 0.50 T at a constant angular speed of 60 revolutions per second.Find the maximum induced emf in the generator.

In an ideal transformer,how many turns are necessary in a 110-V primary if the 24-V secondary has 100 turns?

An ideal step-up transformer doubles a primary voltage of 110 V.What is the ratio of the number of turns in its primary coil to the number of turns in the secondary coil?

You are designing an ac generator with a maximum emf of 8.0 V.If the generator coil has 200 turns,each with a cross-sectional area of 0.030 m2,what should be the frequency of the generator in a magnetic field of 0.030 T?

You wish to construct a simple ac generator with a maximum output of 12 V when rotated at 60 Hz.A magnetic field of 0.050 T is available.If the area of the rotating coil is 100 cm2,how many turns are needed?

The coil of an ac generator has 50 loops and a cross-sectional area of 0.25 m2.What is the maximum emf that can be generated by this generator if it is spinning with an angular speed of 4.0 rad/s in a 2.0-T B⃗\vec { B }B field?

The primary of an ideal transformer has 100 turns and its secondary has 200 turns.If the input voltage to the primary is 100 V,we can expect the output voltage of the secondary to be

A rectangular coil of N turns,length L = 25 cm,and width w = 15 cm,as shown in the figure,is rotating in a magnetic field of 1.6 T with a frequency of 75 Hz.If the coil develops a maximum emf 56.9 V,what is the value of N?

The primary coil of an ideal transformer has 100 turns and its secondary coil has 400 turns.If the ac voltage applied to the primary coil is 120 V,what voltage is present in its secondary coil?

An ac generator with a total resistance of 12 Ω contains 100 flat loops of wire,each with an area of 0.090 m².The loops rotate at 60 rev/s in a $\vec { B }$ field of magnitude 0.50 T.What is the maximum possible induced current?

A circular coil with 600 turns has a radius of 15 cm.The coil is rotating about an axis perpendicular to a magnetic field $\vec { B }$ of 0.020 T in magnitude.If the maximum induced emf in the coil is 1.6 V,at what angular frequency is the coil rotating?

An ac generator consists of 100 loops of wire,each of area 0.090 m²,and has a total resistance 12 Ω.The loops rotate about a diameter in a magnetic field of 0.50 T at a constant angular speed of 60 revolutions per second.Find the maximum induced emf in the generator.

You are designing an ac generator with a maximum emf of 8.0 V.If the generator coil has 200 turns,each with a cross-sectional area of 0.030 m²,what should be the frequency of the generator in a magnetic field of 0.030 T?

You wish to construct a simple ac generator with a maximum output of 12 V when rotated at 60 Hz.A magnetic field of 0.050 T is available.If the area of the rotating coil is 100 cm²,how many turns are needed?

The coil of an ac generator has 50 loops and a cross-sectional area of 0.25 m².What is the maximum emf that can be generated by this generator if it is spinning with an angular speed of 4.0 rad/s in a 2.0-T $\vec { B }$ field?