CHAPTER 3: ELECTRIC CURRENT AND DIRECT CURRENT CIRCUIT PSPM II 2005/2006 NO. 3 3. (a) Write Kirchhoff s law for the conservation of energy. FIGURE 2 (b) A circuit of two batteries and two resistors is as shown in FIGURE 2. Determine the magnitude and direction of current in the circuit. [Ans: I = 0. 14 A ; Anticlockwise] PSPM II 2005/2006 NO. 11(A),(B) 11. (a) Explain how to convert a galvanometer to (i) Voltmeter. Ammeter. [2 marks] (b) A galvanometer has an internal resistance of 25 Ω and a full scale deflection of 5 μa. Calculate (i) the value of the resistor used to convert the galvanometer to voltmeter with a maximum range of 15 V. [Ans: R = 2999975 Ω = 3 MΩ] the power consumed by voltmeter at full scale deflection. [Ans: P = 7. 5 10 5 W] PSPM II 2006/2007 NO. 3 3. (a) FIGURE 2 PCH 1
Based on the voltage-current graph in FIGURE 2, is the conductor ohmic or nonohmic? Justify your answer. (b) A platinum wire has a resistance of 1.5 Ω at 30. Calculate the wire resistance at 100 if the wire temperature coefficient of resistance is 3.92 10 3 1. [Ans: R = 1. 9 Ω] PSPM II 2006/2007 NO. 11 11. (a) State Ohm s law. (b) [1 mark] FIGURE 7 FIGURE 7 shows the arrangement of five equal resistors in a circuit. Calculate (i) The equivalent resistance between point x and y. [Ans: R x y = 8 Ω] The voltage across point b and c. [Ans: V b c = 3 V] (iii) The voltage across point c and y. [Ans: V c y = 9 V] (c) FIGURE 8 The internal resistance of all the batteries in FIGURE 8 are negligible. Calculate the current I 1, I 2 and I 3 when switch S is (i) Open. [Ans: I = 1. 83 A] Closed. [Ans: I 1 = 2. 51 A; I 2 = 1. 15 A; I 3 = 1. 36 A] [8 marks] PCH 2
PSPM II 2007/2008 NO. 3 3. A light bulb has a rating of 230 V and 60 W. Calculate the quantity of charge that passes through the bulb in 3 s. [Ans: Q = 0. 78 C] PSPM II 2007/2008 NO. 11 11. (a) State Kirchhoff s laws. [2 marks] (b) Battery P with emf 1.3 V and internal resistance 2 Ω, battery Q with emf 1.5 V and internal resistance 0.8 Ω, and a 4 Ω resistor are connected in parallel. (i) Sketch the circuit diagram. Calculate the current in battery P, battery Q and the 4 Ω resistor. [Ans: I 1 = 0. 019 A; I 2 = 0. 297 A; I 3 = 0. 316 A] (iii) Calculate the potential difference across the 4 Ω resistor. [Ans: V 4Ω = 1. 26 V] [8 marks] (c) Given a voltmeter, a battery, a known resistor R 1 and an unknown resistor R 2. With the aid of a diagram, describe a method to determine the value of R 2. [5 marks] PSPM II 2008/2009 NO. 3 3. FIGURE 1 Calculate the effective resistance of the circuit in FIGURE 1. [Ans: R = 2. 45 Ω] PCH 3
PSPM II 2008/2009 NO. 11 11. FIGURE 6 FIGURE 6 shows a Wheatstone Bridge with a variable resistor P. (a) Describe how to balance the Wheatstone Bridge. [2 marks] (b) Once the Wheatstone Bridge is balanced, (i) Explain the principles used in determining the resistance of P. Calculate the resistance of P. [Ans: R P = 3. 75 Ω] [7 marks] (c) (i) Explain the need to use high voltage to deliver grid electricity. A copper transmission cable of cross sectional area 7.0 mm 2 is carrying 0.12 A current. If there is an increase in temperature by 15, calculate the power loss per unit length in the cable. [Ans: P l = 3. 7 10 5 W m 1 ] Given: Resistivity of copper = 1.7 10 8 Ω m. Temperature coefficient resistivity of copper = 3.9 10 3 1 PSPM II 2009/2010 NO. 3 3. The dimensions of two copper wires, P and Q are given in TABLE 1. TABLE 1 Wire Length Radius P L r Q 2L r 2 Calculate the ratio of resistance of P to Q. [Ans: R P R Q = 1 8 ] PCH 4
PSPM II 2009/2010 NO. 11 11. (a) An electric bulb is labeled 100 W, 240 V. Calculate the power rating of a bulb with twice the resistance of the 100 W bulb. [Ans: P new = 50 W] (b) FIGURE 5 FIGURE 5 shows a circuit with two batteries, three resistors and a switch. Using the given labeled circuit diagram, determine the ammeter and voltmeter readings when the switch in the circuit is (i) Opened. [Ans: I = 0. 6 A; V = 0 V] Closed. [Ans: I 1 = 1. 154 A; V 3 = 3. 692 V] [12 marks] PSPM II 2010/2011 NO. 3 3. A wire of length 10 m and a diameter of 4 mm has an electrical conductivity of 6.0 10 7 Ω 1 m 1. Calculate (a) the resistivity of the wire. [Ans: ρ = 1. 67 10 8 Ω m] (b) the resistance of the wire. [Ans: R = 0. 013 Ω] PSPM II 2010/2011 NO. 11 11. (a) FIGURE 5 FIGURE 5 shows a circuit with unknown resistor R and emf ε. If the currents in the circuit are as shown, calculate the (i) current I R. [Ans: I R = 8 A] Value of R. [Ans: R = 1 Ω] (iii) Value of ε. [Ans: ε = 10 V] PCH 5
(b) FIGURE 6 FIGURE 6 shows a simple potentiometer. Wire PQ has length 100 cm and resistance 2.4 Ω. The galvanometer G shows no deflection when the jockey is at X, a distance 60 cm from P. (i) By neglecting the internal resistance of the 2.0 V battery, calculate the emf ε B of battery B. [Ans: ε B = 0. 74 V] The galvanometer and battery B are replaced by a voltmeter of internal resistance 20 Ω. Calculate the reading of the voltmeter if the jockey is maintained at its position, X. [Ans: V PX = 0. 71 V] [8 marks] (c) For a Wheatstone bridge, (i) Sketch and label the circuit. Write the resistance equation when the bridge is balanced. (iii) State one of its application. PSPM II 2011/2012 NO. 2 2. (a) State Ohm s law. [1 mark] (b) A potential difference of 15 V is applied across a uniform wire of length 2.80 m and radius 0.30 cm. If 0.60 A current flows in the wire, calculate (i) the resistance of the wire. [Ans: R = 25. 0 Ω] the resistivity of the wire. [Ans: ρ = 2. 5 10 4 Ω m] (c) FIGURE 2 PCH 6
Two batteries and four resistors are connected in a circuit where currents I 1, I 2 and I 3 flow as shown in FIGURE 2. (i) Calculate I 1, I 2 and I 3. [Ans: I 1 = 1. 85 A ; I 2 = 0. 23 A ; I 3 = 1. 62 A] What does it imply if the calculated current is negative? (iii) Calculate the potential difference between points X and Y. [Ans: V X V Y = 4. 16 V] (iv) Calculate the total power dissipated in the circuit. [Ans: P = 20. 9 W] [11 marks] PSPM II 2012/2013 NO. 2 2. (a) (i) Define the emf of a battery. A battery has an emf of 12 V and internal resistance r is connected to a resistor R = 4 Ω. The voltage across the battery terminal is measured to be 8 V. Calculate the internal resistance. [Ans: r = 2 Ω] (b) FIGURE 3 FIGURE 3 shows a circuit consisting of batteries with internal resistance 6 V, 1 Ω and 10 V, 2 Ω and connected to resistors of 8 Ω, 9 Ω and 12 Ω. By using the anticlockwise loop as shown, calculate (i) The current that flows through the 8 Ω resistor. [Ans: I = 0. 5 A] The potential difference between point A and C, V AC. [Ans: V AC = 5. 5 V] (c) The heating element is made of 1.0 m long wire with cross-sectional area of 3.1 10 6 m 2. The wire has a resistivity of ρ 0 = 6.8 10 5 Ω m at a temperature T 0 = 320 and a temperature coefficient of resistivity α = 2.0 10 3 K 1. (i) (iii) Define temperature coefficient of resistivity, α. Determine the resistance of the heating element at an operating temperature of 420. [Ans: R = 26. 3 Ω] If the heating element is connected to 100 V power supply, is the power dissipated at 320 and 420 are the same? Justify your answer. [Ans: Power is same/unchanged.] PCH 7
PSPM II 2013/2014 NO. 2 2. (a) (i) State ONE application of a Wheatstone bridge. Explain the principle used in such application. FIGURE 3 State TWO laws to be used in determining the currents in the circuit as shown in FIGURE 3. [5 marks] (b) A toaster has a heating element made of nichrome wire and connected to a 220 V source. The wire is initially at 20 with current 1.8 A. When the toaster reaches its final operating temperature, the current is 1.53 A. Calculate the (i) power delivered to the toaster at its operating temperature. [Ans: P = 336. 6 W] final temperature of the heating element if the temperature coefficient of resistivity for nichrome wire is 4 10 4 1. [Ans: T = 461 ] (c) The emf of a battery with internal resistance is 12 V. When an unknown resistor R is connected to the battery, the current is 0.8 A. If another resistor R is added in series, the current is 0.6 A. Calculate the (i) (iii) value of the resistor R. [Ans: R = 5 Ω] internal resistance of the battery. [Ans: r = 10 Ω] Terminal voltage of the battery. [Ans: V terminal battery = 6 V] PSPM II 2014/2015 NO. 2 2. (a) FIGURE 3 PCH 8
FIGURE 3 shows some of the free electrons inside a section of a cylindrical copper wire. The wire is connected to an emf source, and the direction of the electric field, E is as indicated in the figure. (i) Sketch a diagram to show the motions of one free electron, the directions of drift velocity and the current. If the current in the wire is 50 ma, calculate the number of electrons passing a point in 10 s. [Ans: n = 3 10 18 ] [5 marks] (b) A battery has an emf of 9 V. The terminal voltage is 8 V when the battery is connected across a resistor of 5 Ω. Calculate the (i) current through the resistor. [Ans: I = 1. 6 A] power dissipated by the resistor. [Ans: P = 12. 8 W] (iii) Internal resistance of the battery. [Ans: r = 0. 625 Ω] (c) FIGURE 4 By referring to FIGURE 4, determine (i) I 1, I 2 and I 3. [Ans: I 1 = 0. 15 A; I 2 = 0. 52 A; I 3 = 0. 67 A] The potential difference across the 18 Ω resistor. [Ans: V 18 = 12 V] [7 marks] PCH 9