Physics 133: tutorial week 5 Alternating currents, magnetic fields and transformers.

Size: px

Start display at page:

Download "Physics 133: tutorial week 5 Alternating currents, magnetic fields and transformers."

Arthur Page
7 years ago
Views:

1 Physics 133: tutorial week 5 Alternating currents, magnetic fields and transformers. 61. In the wires connecting an electric clock to a wall socket, how many times a day does the alternating current reverse its direction if run off South African mains? ( ) The current reverses direction twice per cycle and there are 50 cycles per second. The number of reversals per day is therefore 50 times the number of seconds in a day: Reversals per day = ( 50) = Calculate the peak current passing through a 60W light bulb connected to a 40V ac supply. (0.354A) I rms = P = 60 = 0.5 A. V rms 40 I 0 = I rms = 0.5 = A. 63. An ac voltage, whose peak value is 90V, is across a 35 Ï resistor. What is the value of the peak and rms currents in the resistor? (.57A; 1.8A) I 0 = V 0 R = 90 =.57 A. 35 I rms = I 0 =.57 = 1.8 A. 64. Suppose that a current is given by the equation: I =.5 sin(10t) (with I in amps and t in seconds). (a) What is the frequency? (b) What is the rms value of the current? (c) If this current is through a 50 Ï resistor, what is the equation that describes the voltage as a function of time? (a) πf = 10 Hz f = 19.1 Hz. (b) I 0 =.5 V I rms =.5 = 1.77 A. (c) V 0 = I 0 R =.5 50 = 15 V V = 15 sin(10t)volts. (19.1 Hz; 1.77 A; 15 sin(10t) volts)

2 65. A wire 1.0m long carries a current of 10A and makes an angle of 30 with a uniform magnetic field with = 1.5T. Calculate the magnitude and direction of the force on the wire. (7.5N, perpendicular to both the wire and to ) = Il sin θ = sin 30 = 7.5 N. Using the right hand push rule for the configuration depicted on the right, the force is into the page, at right angles to both the field and the wire (a) Calculate the force per unit length on a wire carrying a current of 0.5A when perpendicular to a 4.0T magnetic field. (b) What if the angle between the wire and the field is 45? (.0Nm 1 ; 1.41Nm 1 ) (a) The wire is perpendicular to the field, therefore θ = 90 and sinθ = 1 hence = Il. The force per unit length is: l = I = =.0 Nm 1. (b) l = I sinθ = sin 45 = 1.41 Nm The force on a wire carrying 0A is a maximum of 3.6N when placed between the pole faces of a magnet. If the wire is 15cm long, what is the approximate magnitude of? (1.T) The force is a maximum when the angle the wire makes with the field is 90. Hence = Il = = 1. T. 68. How much current is flowing in a wire.0m long if the maximum force on it is 0.7N when placed in a uniform 0.03T field? (11.7A) Since force is a maximum, the angle between the wire and the field is 90. Hence I = l = 0.7 = 11.7 A Calculate the magnetic force on a 140 m length of wire stretched between two towers carrying a 00A current. The earth s magnetic field of T makes an angle of 60 with the wire. (1.1N) = Il sin θ = sin 60 = 1.1 N. 70. Calculate the magnitude of the magnetic field, 3cm from a long, straight wire carrying 8.0A. ( T) = k I r = = T. 71. How much current does a wire carry if = 0.03T at a point 1cm from it? (18000A) I = r k = = A.

3 7. How far from a long, straight wire carrying 10A will the magnetic field be T? (0.0mm) r = ki = = 10 4 m = 0.0 mm. 73. Determine the magnetic field midway between two long, straight wires 10 cm apart if one carries 10A and the other 8.0A and these currents are (a) in the same direction, and (b) in opposite directions. ( T; T) (a) Midway between the wires, the field due to each wire is perpendicular to the line joining the wires. When the current in the wires is in the same direction, the fields are in opposite directions. Hence { I1 = 1 = k r I } { 10 = 10 7 r } = T (b) When the wires carry current in the opposite direction, the fields are in the same direction, hence = 1 + = k { I1 r + I } r { 10 = } 0.05 = T. 74. Two long, fixed vertical wires A and are 50cm apart and carry currents of 100A and 60A respectively in opposite directions. Determine (a) the force per unit length exerted by wire A on wire, (b) the magnetic field at P 100cm from A and 150cm from, and (c) the position of any neutral point in a horizontal plane. ( Nm 1 away from A; T; 75cm from and 15cm from A) (a) l = ki AI = = Nm 1 (away from A). L 0.50 (b) The point 100cm from A and 150cm from lies on the line joining A and since the wires are 50cm apart. The field due to both wires at this point is therefore perpendicular to the line joining the wires. urthermore, The fields here are in opposite directions. Hence { IA = A = k I } { 100 = 10 7 r A r } = T. 1.5 (c) There will be a neutral point where A =, a distance x from A so that r A = x and r = x 0.5(we take x 0.5 instead of x+0.5 since the neutral point lies closer to than to A because the field due to A is stronger than the field due to ). Hence k I A = k I 100 gives r A r x = 60 so that x = 1.5 m. x 0.5

4 75. Two long, parallel wires 1 cm apart carry 15 A currents in the same direction. Determine the magnitude of the magnetic field at a point 10cm from one wire and 0cm from the other. (Hint: make a drawing in a plane containing the field lines and recall the rules for vector addition.) ( T) R R A P A 0 cm 10 cm A 1 cm P θ A A and denote the magnetic fields at point P: they are tangential to the circles centred at A and respectively. R is the resultant. A = k I A = r A 0.10 = T. = k I = r 0.0 = T, and R = A + A cosφ. Here φ = PA R = 180 θ, since PA R is a parallelogram with P = R = θ. In PA, 1 = cosθ, which gives cosθ = cosφ = inally, R = ( ) = T. 76. Calculate the magnitude and direction of the force between two parallel wires 85 m long and 30cm apart, each carrying 60A in the same direction. (0.04N attractive) l = ki 1I = = 0.04 N. L A vertical, straight wire carrying 5A exerts an attractive force per unit length Nm 1 on a second, parallel wire 8.0cm away. What current (magnitude and direction) flows in the second wire? (48A) l = ki 1I L I = l L = ki = 48 A. 5

5 78. A transformer changes 1V to 18000V and there are 6000 turns in the secondary. How many turns are there in the primary? (4) n p = n s V p V s = = A transformer has 145 turns in the primary and 55 in the secondary. What kind of transformer is this, and by what factor does it change the voltage? (step down; 0.379) n s This is a step-down transformer, with = 55 n p 145 = A step-up transformer increases 30 V to 10 V. What is the current in the secondary as compared to the primary? (I S = I P /4) I s = n p = 30 I s = 1 I p n s 10 4 I p 81. Describe a transformer that could be used to light a 6V bulb from a 40V, 50Hz source. (step down; turns ratio of 40) We require a step-down transformer with V s V p = 6 40 = 1 40 = n s n p. 8. A transformer has 1500 primary turns and 10 secondary turns. The input voltage is 40 V and the output current is 8.0 A. What is the secondary voltage and primary current? (19. V; 0.64 A) n p = 1500 n s 10 = V p = 40 V s V s V s = = I s I p = 8.0 I p = 19. V and I p = = 0.64 A.

104 Practice Exam 2-3/21/02

104 Practice Exam 2-3/21/02 1. Two electrons are located in a region of space where the magnetic field is zero. Electron A is at rest; and electron B is moving westward with a constant velocity. A non-zero