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son4ous [18]
3 years ago
6

In a physics laboratory experiment, a coil with 250 turns enclosing an area of 11.6 cm2 is rotated during the time interval 3.90

×10−2 s from a position in which its plane is perpendicular to Earth's magnetic field to one in which its plane is parallel to the field. The magnitude of Earth's magnetic field at the lab location is 7.00×10−5 T .
Physics
2 answers:
dolphi86 [110]3 years ago
6 0

Answer:

a) Ф_{B.i} =  8.1 X 10^{-8} Wb, Ф_{B.f} = 0

b) E = 0.52mV

Explanation:

a) considering the loop of wire which has an area of A = 11.6cm² and N = 250 turns, it is initially placed perpendicularly in the earth magnetic field. Then it is rotated from this position to a position where its plane is parallel to the field as shown in the following figure in Δt = 0.040s. Given that the earths magnetic field at the position of the loop is B = 7.0 x 10^{-5 } T, the flux through the loop before it is rotated is:

Ф_{B.i} = BAcos(Ф_{i}) = BAcos(0°)

Ф_{B.i} =(7.0 x 10^{-5 } T)(11.6 x 10^{-4} m^{2})(1)

Ф_{B.i}  = 8.1 X 10^{-8} Wb

Ф_{B.i} =  8.1 X 10^{-8} Wb

after it is rotated the angle between the area and the magnetic field is Ф = 90°, hence

Ф_{B.f} = BAcos(Фf) = BAcos(90°) = 0

b) The average magnitude of the emf induced in the coil equals the change in the flux divided by the time of this change, and multiplied by the number of turns that is

|Eav| = N | ФB,f - ФB,i |/ Δt

=|E_{av} | =250 \frac{0-8.1X 10^{-8} }{3.90 X 10^{-2} }

= 5.2 x 10^{-4} V

E = 0.52mV

Virty [35]3 years ago
3 0

Answer:

a) Φin = 8.12x10⁻⁸ Wb

b) Φfin = 0

c) ε = 5.2x10⁻⁴ V

Explanation:

a) The total magnitude of magnetic flux before it is rotated is equal

Φin = B*A*sinθ

B = 7x10⁻⁵ T

A = 11.6 cm² = 0.00116 m²

Replacing

Φin = 7x10⁻⁵ * 0.00116 * sin90° = 8.12x10⁻⁸ Wb

b) The toal magnitude of magnetic flux after it is rotated

Φfin = B*A*sinθ = 7x10⁻⁵ * 0.00116 * sin0° = 0

c) Magnitude of the average emf induced is equal to:

e = N(\frac{O_{in}-O_{fin}  }{t} )=250(\frac{8.12x10^{-8}-0 }{3.9x10^{-2} } )=5.2x10^{-4} V

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The question incomplete! The complete question along with answer and explanation is provided below.

Question:

Augment the rectifier circuit of Problem 4.68 with a  capacitor chosen to provide a peak-to-peak ripple voltage of  (i) 10% of the peak output and (ii) 1% of the peak output. In  each case:

(a) What average output voltage results?

(b) What fraction of the cycle does the diode conduct?

(c) What is the average diode current?

(d) What is the peak diode current?

Problem 4.68:

A half-wave rectifier circuit with a 1-kΩ load operates from a 120-V (rms) 60-Hz household supply through  a 10-to-1 step-down transformer. It uses a silicon diode  that can be modeled to have a 0.7-V drop for any current.

Given Information:

Input voltage = 120 Vrms

10 to 1 step-down transformer

Voltage drop at diode = 0.7 V

Load resistance = R = 1 kΩ

Required Information:

 (i) 10% of the peak output and (ii) 1% of the peak output. In  each case:

(a) What average output voltage results?

(b) What fraction of the cycle does the diode conduct?

(c) What is the average diode current?

(d) What is the peak diode current?

Answer:

Case (i)

Vavg = 15.45 V

Conduction of diode = 7.11 %

Iavg = 0.232 A

Ip = 0.449 A

Case (ii)

Vavg = 16.18 V

Conduction of diode = 2.25 %

Iavg = 0.735 A

Ip = 1.453 A

Explanation:

Voltage at the secondary side of the transformer is

Vrms = Vpri/turn ratio

Vrms = 120/10 = 12 V

The relation between rms voltage and peak voltage is

Vp = Vrms/√2

Vp = 12√2 = 16.97 V

Vd = 0.7 V

First we will calculate all the required parameters for the 10% ripple voltage and then for 1% ripple voltage.

case (i) 10% of the peak output:

(a) What average output voltage results?

Average output voltage = Vavg = Vp - Vd - 0.5Vr

Where Vp is the peak output voltage Vd is the voltage drop of diode and Vr is the ripple voltage which is given as a percentage of Vp

Vavg = Vp - Vd - 0.5Vr

Vavg = 16.97 - 0.7 - 0.5[0.1(16.97 - 0.7)]

Vavg = 15.45 V

(b) What fraction of the cycle does the diode conduct?

ω = √2Vr/Vp - Vd

ω = √2*0.1(Vp-Vd)/Vp - Vd

ω = √2*0.1(16.97-0.7)/16.97 - 0.7

ω = 0.447 rad

Conduction of diode = (ω/2π)*100

Conduction of diode = (0.447/2π)*100

Conduction of diode = 7.11 %

(c) What is the average diode current?

Average current = Iavg = Vavg/R[ 1 + π( √2(Vp - Vd)/0.1(Vp-Vd))]

Average current = Iavg = 15.45/1000[ 1 + π( √2(16.97 - 0.7)/0.1(16.97-0.7))]

Average current = Iavg = 0.232 A

(d) What is the peak diode current?

Peak current = Ip = Vavg/R[ 1 + 2π( √2(Vp - Vd)/0.1(Vp-Vd))]

Peak current = Ip = 15.45/1000[ 1 + 2π( √2(16.97 - 0.7)/0.1(16.97-0.7))]

Peak current = Ip = 0.449 A

case (ii) 1% of the peak output:

(a) What average output voltage results?

Vavg = 16.97 - 0.7 - 0.5[0.01(16.97 - 0.7)]

Vavg = 16.18 V

(b) What fraction of the cycle does the diode conduct?

ω = √2*0.01(Vp-Vd)/Vp - Vd

ω = √2*0.01(16.97-0.7)/16.97 - 0.7

ω = 0.1417 rad

Conduction of diode = (0.1417/2π)*100

Conduction of diode = 2.25 %

(c) What is the average diode current?

Average current = Iavg = 16.18/1000[ 1 + π( √2(16.97 - 0.7)/0.01(16.97-0.7))]

Average current = Iavg = 0.735 A

(d) What is the peak diode current?

Peak current = Ip = 16.18/1000[ 1 + 2π( √2(16.97 - 0.7)/0.01(16.97-0.7))]

Peak current = Ip = 1.453 A

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