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FAKULTI KEJURUTERAAN ELEKTRONIK DAN KEJURUTERAAN KOMPUTER BENT 2713- CIRCUIT THEORY 1 TUTORIAL 1 1. Complete the unit prefix table 1-2, for the following values. Table 1-2 Units Powers of 10 Metric Prefix Symbol 1,000,000,000 109 giga G 1,000,000 106 mega M 1,000 103 kilo k 100 1 .001 10-3 milli m .000001 10-6 micro µ .000000001 10-9 nano n 2. When plugged into a 120 V wall outlet, an electric lamp draws 1.25 A. What it is resistance? By Ohm’s Law, = = = . = Ω 3. A relay with a coil resistance of 240 requires a minimum of 50 mA to operate. What is the minimum voltage that will cause it to operate? Again, by Ohm’s Law, = = − = Ω 4. A 120 V electric coffee maker is rated 960 W. Determine its resistance and rated current. = = By Ohm’s Law, = = = = = = Ω 5. Determine the current flowing through an element if the charge flow is given by: a) () = (3 + 8) b) () = (8 2 + 4 − 2) c) () = (3 − − 5 −2 ) d) () = 10120 6. (a) i = (b) i = (c) i = (d) i = dq dt = = = = dq (3 + 8) = 3 (8 2 + 4 − 2) = 2(8) + 4 = (16 + 4) (3 − − 5 −2 ) = [−3 − − (−2)(5 −2 )] = (−3 − + 10 −2 ) (10 sin120πt) = [120π(10) cos 120πt] pA = (1200 π cos120πt)pA dt Find the charge flowing through a device if the current is: a) () = 3, (0) = 1 b) () = (2 + 5), (0) = 0 c) () = 20 (10 + ⁄6), (0) = 2 (a) q(t) = ∫ . = ∫ 3. = [3 + ] Find c: t=0, q(0)= 1 q(0)=3(0)+c → c= 1 q(t) = (3t + 1) C (b) q(t) = ∫ . = ∫(2 + 5) = [ 2 2 2 + 5 + ] Find c: t=0, q(0)= 0, so c=0 q(t) = (t2 + 5t) mC (c) q(t) = ∫ . = ∫[20 cos(10 + 6 ) = 20 ∫ cos (10 + 6 ) let u = 10t + du = 10dt 6 Then, 1 = 10 q(t) = ∫ = 20 cos() . du 10 20 ∫ cos . 10 = 2(sin ) = 2 [sin(10 + )] + 6 Find c: t=0, q(0)= 2µC q(0) = 2 [sin(10 + )] + 6 180 2µC = 2 [sin(0 + )] + = (2 sin 300 + )µ 6 2µC = (2 sin 300 + )µ c = (2 − 1)µ = 1µ q(t) = [2sin(10 + ) + 1] µC 6 7. If the function f(t) in Figure 1 is the current in amperes entering the positive terminal of an element at time t (seconds), find: a) The total charge that has entered between 4 and 9 s, b) The charge entering at 8 s, and c) The current at 1, 5 and 8 s. Take the charge to be 0 at t = 0. f(t) 8 6 2 0 4 6 7 Figure 1 9 12 t (s) 8. The charge flowing in a wire is plotted in Figure 2 below. Sketch the corresponding current. Figure 2 9. Figure 3 shows the current through and the voltage across a device. (a) Sketch the power delivered to the device for t >0 (b) Find the total energy absorbed by the device for the period of 0 < t < 4s. Figure 3 10. A rechargeable flashlight battery is capable of delivering 85 mA for about 12 h. How much charge can it release at that rate? If its terminal voltage is 1.2 V., how much energy can the battery deliver? 11. The current entering the positive terminal of a device is () = 3 −2 , and the voltage across the device is () = 5 ⁄ a) Find the charge delivered to the device between = 0 and = 2 b) Calculate the power absorbed c) Determine the energy absorbed in 3 . 12. Figure 4 shows a circuit with 5 elements. If 1 = −205 , 2 = 60 , 4 = 45 , 5 = 30 , calculate the power 3 received or delivered by element 3. Figure 4 13. Consider the circuit of Figure 5. The power consumed by each resistor is as follows: p2(t) = 98 W, p3(t) = 12 W, p4(t) = 16 W, p5(t) = 768.8 W, and p6(t) = 486 W. The subscript corresponds to the resistor value. (a) For each resistor, determine the indicated voltage or current. (b) Determine the total power delivered by the two sources. (c) Determine the value of Vin and the value of Iin. Explain your reasoning. 2Ω + V2 I3 + V4 3Ω Vin 4Ω I5 5Ω Figure 5 Iin 6Ω + V6 - 14. Find in the network. 15. Find 0 in the circuit 16. Find v and i. 2Ω 2A 3Ω 6V 3Ω 2Ω + 8V v i 17. Find i and vab. b a i 1A 2Ω 5Ω 12 V 3Ω 6Ω + 6V 3A 1A 4Ω 18. A 1.8 kW electric heater takes 15 min to boil a quantity of water. If this is done once a day and power costs 10 cents/kWh, what is the cost of its operation for 30 days? 19. An electric stove with 4 burners and an oven is used in preparing a meal as follows: a) Burner 1 : 20 min b) Burner 2 : 40 min c) Burner 3 : 15 min d) Burner 4 : 45 min e) Oven : 30 min If each burner is rated at 1.2 kW and the oven at 1.8kW, and electricity cost 12 cents per kWh, calculate the cost of electricity used in preparing meal. 20. By referring to Figure 6, find the following: (a) What is the resistance across the terminals ab of the network shown? (b) Calculate the voltage across the terminals ac if a 36-V battery is connected across the terminals ab. (c) Calculate the power dissipated in the 9-Ω resistor connected across ab and in the 9-Ω resistor connected across bc of the network when a 36-V source is connected across ab. 9Ω a 6Ω c 6Ω 9Ω 9Ω 6Ω b Figure 6