ASSOCIATE DEGREE IN ENGINEERING TECHNOLOGY RESIT EXAMINATIONS SEMESTER 2 JUNE 2011

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1 ASSOCIATE DEGREE IN ENGINEERING TECHNOLOGY RESIT EXAMINATIONS SEMESTER 2 JUNE 2011 COURSE NAME: PHYSICS 2 CODE: GROUP: ADET 1 DATE: JUNE 29 TIME: 1:00 DURATION: 2 HOUR INSTRUCTIONS: 1. This paper consists of SIX questions. 2. Candidates must attempt ANY FOUR questions on this paper. 3. All working MUST be CLEARLY shown. 4. Keep all parts of the same question together. 5. The use of non-programmable calculators is permitted. DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO 1

2 Instructions: Answer any FOUR (4) questions. [Question 1] a. i. State Coulomb s Law. Give the meaning of each symbol used. State the formula for the electric field and potential at a distance r from a point charge Q. b. The force between two identical charges and distance apart is 10 N. Calculate the force between two identical charges (where ) when their distance of separation is. [6] c. Find the net force acting on the charge and the electric potential energy for the following array of charges: Charge is located at charges is located at and charge is located at [15] [Question 2] a. State the formula for the capacitance of a parallel plate capacitor with a dielectric between it plates. Give the meaning of each symbol used. b. A parallel plate capacitor has a capacitance of, a plate separation of 2 mm and the area of each plate is. Give the potential difference between the plates is 80 V, determine : i. The dielectric constant The charge on either plate i The energy stored in the capacitor [6] 2

3 c. Derive the effective capacitance for two capacitors and connected in series and then in parallel. [4] d. The circuit show an arrangement of four capacitors connected to a 12 V battery. i. Determine the equivalent capacitance of the capacitors in the circuit, relative to the battery terminals. Calculate the charge on the 3.0 pf capacitor. i Show that the charge on the 8.0 pf capacitor is 12 pc. iv. How much energy is stored in the 8pF capacitor [13 marks] 3

4 [Question 3] a. Write down the formula for the effective resistance of two resistors when they are connected in (i) series and (ii) parallel. b. Two resistors have resistances and. When the resistors are connected in series to a 18.0 V battery, the current from the battery is 2.00 A. When the resistors are connected in parallel to the 18.0 V battery the total current from the battery is 9.00 A. Find the values of and. [7] c. If a 93.5 V emf is connected to the terminals A and B in the figure below and the current in the 4.0 resistor is 17 A, what is the value of the unknown resistor R? A R Emf 2.0Ω 1.0Ω B 4.0Ω [8] d. Consider a battery with EMF E and the internal resistance r. Its terminal voltage is 11 V when connected in series with a 11 Ω resistor and 10 V when connected in series with a 5 Ω resistor. Determine r. [8] 4

5 (Question 4) a. State Kirchhoff s laws. b. For the circuit shown in the figure below use Kirchhoff s laws to calculate: i. The current flowing in each branch of the circuit [8] The potential difference across the 5 Ω resistor. 1.5Ω 6 V 5Ω 2Ω 4.5 V c. The Wheatstone bridge circuit shown below is used to measure the unknown resistance. When is adjusted so that no current flows through the galvanometer the value of can be determine. i. Determine in terms of and. If the Wheatstone bridge is balanced when and, determine the value of. [8] 5

6 B A G C D d. An alternating voltage is represented by the expression volt. Determine, i. the maximum value. i the frequency. the period of the wave form and iv. the value 3.5 ms after it passes through zero, going positive. [5] (Question 5) a. State Faraday s and Lenz s laws of electromagnetic induction. [4] b. The magnetic field B at a distance r from a very long straight wire carrying a current I is given by The figure below shows three very long, straight, parallel wires carrying currents perpendicular to the plane of the paper, as shown. Here, the point P is 4.0 cm from all three wires. Calculate the magnitude and direction of the resultant magnetic field at P due to i. The wires 1 and 2. [4] The wires 1, 2 and 3 [6] 6

7 c. Write down an expression for the magnetic field strength in a solenoid in terms of the current flowing, number of loops (turns) per unit length and permeability of free space. A 1000-turn solenoid with a length of 50 cm and radius 2 cm carries a current of 3 A. A second coil of 100 turns is wrapped tightly around the middle region of the solenoid such that the coil can be considered to have the same radius as the solenoid. i. Calculate the magnetic field strength in the solenoid at 3 A. Find the change in the magnetic flux through the coil and the average induced emf in the coil when the current in the solenoid increases to 6.0 A in a time of 2.0 s.[5] i Calculate the induced current through the coil if its resistance is 5.0 Ω. [3] (Question 6) a. Explain what is meant by i. Mass defect, Binding energy of an atomic nucleus [4] b. An alpha particle decay converts to. i. Write the equation for the decay process. [3] Calculate the energy (in MeV) released. [3] Mass of, Mass of, and Mass of, 7

8 c. In the radioactive decay series starting with thorium and ending with bismuth, calculate the total number of alpha particles and beta particles that are generated. [7] d. Define the following terms, i. Activity Half-life i A small volume of a solution which contained a radioactive isotope of sodium had an activity of 12,000 disintegrations per minute when it was injected into the bloodstream of a patient. After 30 hours the activity of of the blood was found to be 0.50 disintegrations per minute. If the half-life of the sodium isotope is taken as 15 hours, estimate the volume of blood in the patient. [6] ****END OF PAPER***** 8

9 ASSOCIATE DEGREE IN ENGINEERING SOLUTIONS SEMESTER DECEMBER COURSE NAME: PHYSICS 2 CODE: [8 CHARACTER COURSE CODE] GROUP: AD-ENG 1 DATE: "[EXAM DATE]" TIME: DURATION: 2 HOUR Solutions [Question 1] a. i. The force of attraction or repulsion between two charged bodies is directly proportional to the product of the charges and inversely proportional to the square of the distance between their centres. i b. N [3] 9

10 c. 4m 3 3m 5m N SE Electric potential energy [5] [Question 2] a. A is the area of the plates d is the distance between the plates is the permittivity of the medium 10

11 b. i. i F/m C J c. When capacitors are connected in parallel each capacitor will take a charge from the supply according to its capacitance. But the total charge and where is the total capacitance in the circuit. Thus dividing throughout by V we have When capacitors are connected in series each capacitor will have the same charge but the supply voltage will be divided between the capacitors depending in their capacitances. Also ; and Thus dividing throughout by we have d. i. the 8 pf and 4 pf capacitors are in parallel therefore their total capacitance is 12 pf. Now we have 12 pf, 3 pf and 4 pf capacitors in series therefore the effective capacitance in the circuit is given by [5] Total charge in the circuit Therefore charge on 3 pf is 18 pc [3] i Voltage across 8 pf Charge on 8 pf [3] iv. Energy stored in the 8 pf 11

12 [Question 3] a. i. resistors in series i resistors in parallel b. When the resistors are in series When the resistors are in parallel and Therefore the resistors have values 3Ω and 6Ω c. Voltage across 4 Ω resistor Voltage across 2 Ω resistor Current through 2 Ω resistor Current through 1 Ω resistor and R resistor Voltage across resistor R and 1 Ω resistor is 25.5 V parallel to 2 Ω same voltage voltage across 1 Ω resistor therefore voltage across R is d. (Question 4) a. The algebraic sum of the currents at a junction of a circuit is zero. Round a loop the algebraic sum of the e.m.f.s is equal to the algebraic sum of all the p.d.s in the circuit. b. 12

13 i. By KVL Loop ABEFA:...(1) By KVL loop CBEDC: c. i. and and Dividing both equations 13

14 d. volt i. volts Hz i ms iv. When ms volts V (Question 5) a. The induced emf is proportional to the rate of change of the magnetic flux linking the coil or circuit. The induced current flows always in such a direction as to oppose the change causing it. [4] b. i. T T Resultant magnetic field direction north T Resultant magnetic field [4] Direction to the horizontal NW 14

15 c. i. When I = 6 A Change in magnetic flux Wb (Question 6) Induced emf i Induced current [3] a. i. The difference between the mass of the nucleus of an atom and the sum of the masses of the individual nucleons when they are separated. The energy or work needed to just take all the nucleons apart so that they are completely separated. b.. [3] Mass of, Mass of, Mass converted to energy = u [3] c. [4] Four alpha and one beta d. i. The rate of the nuclear disintegration or decay of an element. the time taken for the atoms to disintegrate to half of the initial number. i after two half-life activity in is 0.5 proportional to 3000 therefore by ratio [6] 15