Solved Problems. Electric Circuits & Components. 11 Write the KVL equation for the circuit shown.


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1 Solved Problems Electric Circuits & Components 11 Write the KVL equation for the circuit shown. 12 Write the KCL equation for the principal node shown. 12A In the DC circuit given in Fig. 1, find (i) i 1 (i) i 2 and (i) i 3.
2 13 Find I out and V out in the network circuit shown. 13A For the DC circuit given in the figure, find the (i) voltage v ab, and (ii) current i L when α = 0.9 and v s = 10V. 14 The source voltage in the circuit is 10V and R 1 = R 2 = 1kΩ. Αssuming a real circuit, with source impedance = 50Ω and impedance across the voltage meter = 1MΩ, determine the voltage in the meter.
3 15 Find the steady state current flowing through the capacitor. 16 Find the input impedance of the circuit. Assume that the circuit operates at ω = 50 rad/s. o 16A In the AC circuit given, v = 120 cos(1000t + 90 ), R = 15Ω, C = 83.3 μf, L = 30mH. Find find (i) i R (i) i C and (i) i L in phasor form. 17 Find the average power delivered from a sinusoidal voltage source of V = 110<0 o > V to an impedance of Z = j Ω. Determine also the power factor. 18 In the circuit shown, find the average power supplied by the source and the average power absorbed by the resistor.
4 19 In the circuit with the ideal transformer shown, find the voltage Vo and the impedance as seen from the source side of the transformer.
5 Laplace Transforms 21 Derive the Laplace transform for (a) u(t), (b) e at u(t). 22 Obtain the Laplace transform of f ( t) 2t = δ( t) + 2u( t) 3e. 23 Find the inverse Laplace transform for ( 4 5s F s) = 1+ s + 3 s Find v o (t) in the circuit shown assuming zero initial conditions. 25 The output in a linear system is y(t) = 10e t sin4t u(t) when the input is x(t) = e t cos4t u(t). Find the transfer function of the system and its impulse function. 26 Determine the transfer function of the circuit shown.
6 Design Problem The US space shuttle delivers parts to build up a space station. The control circuit is shown. The electromagnet coil L for opening and closing the cargo door requires 0.1A before activating. The activating current is i 1 (t). The time required for i 1 to reach 0.1A is less than 3 seconds. Check if this condition is satisfied for L = 1H. Key Assumption The two switches are thrown at t = 0 and they occur instantaneously. Switches prior to t = 0 were in position for a long time.
7 Operational Amplifier 31 A diode has the voltage current relationship as shown. Find the current flowing through the 100Ω resistor in the two circuits using this diode. 32 A 741 op amp has an openloop voltage gain of 2 x 10 5 and used in the circuit shown. Find the closedloop gain and current i o when v s = 1V.
8 33 For the inverting op amp circuit shown v i = 0.5V. Calculate (a) the output voltage v o, and (b) the current in the 10kΩ resistor. 34 For the op amp circuit shown, calculate the output voltage v o. 35 Calculate v o and i o in the op amp circuit shown. 36 Design an op amp circuit with inputs v 1 and v 2 such that v o = 5v 1 + 3v 2.
9 System Modeling 41 Find the electrical analogy for the mechanical system described. 42 Find the electrical analogy for the mechanical system described.
10 System Response 51 For the RC circuit shown, obtain the transfer function and its frequency response. Let v s = V m cosωt. 52 Determine the type of filter of the following RC circuit. 53 In the circuit shown, determine the type of filter (a) in stage 1, (b) in stage 2, and (c) overall.
11 Sensors 61 A strain gage R 3 is connected to the Wheatstone bridge shown. The resistors used in the circuit have the following values at balance: R 1 = 1 k Ω, R 2 = 120 Ω, R 3 = 120 Ω, R 4 = 1 k Ω, R 5 = 1 k Ω, R 6 = 1 k Ω, R 7 = 50 Ω, R 8 = 50 Ω. The bridge is driven by a voltage of V = 5 volts and the gage factor is Find (i) the meter reading value E, and (ii) the actual strain value, when R 3 increases by 1 Ω. 62 An accelerometer has a seismic mass of 0.05kg and a spring constant of 3 x 10 3 N/m. The maximum mass displacement is 0.02m. Calculate (a) the maximum measurable acceleration, and (b) the natural frequency. 63 An RTD has α o = 0.005/ o C, R T = 500Ω at 20 o C. It is placed in a Wheatstone bridge wherein R 1 = R 2 = 500Ω. R 3 is a variable resistor used to null the bridge. Find the resistance of R 3 at 0 o C.
12 64 A thermistor has a resistance of 3.5kΩ and a dissipation constant P D = 5mW/ o C at 20 o C. It is driven by a voltage of 10V. Find the temperature rise in the thermitor due to selfheating. 65 A voltage of 23.72mV is measured in a type K thermocouple at 0 o C reference. Find the temperature of the measurement junction.
13 Actuators 71 A stepper motor has 10 o per step and must rotate at 250rpm. What is input pulse rate (pulses per second) needed to operate? 72 A servomotor has the following performance curves. It is supposed to be able to provide a torque of 0.4Nm from rest to carry a constant load torque of 0.1Nm at an angular acceleration of at least 5rad/s 2. The polar moment of inertia of the rotating components is 0.05kgm 2. At its typical operation, the motor should be rotating at 1600rpm to deliver a torque and output power of at least 0.42Nm and 80Watts respectively. Determine if the motor is able to perform to these specifications.
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