# Solved Problems. Electric Circuits & Components. 1-1 Write the KVL equation for the circuit shown.

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1 Solved Problems Electric Circuits & Components 1-1 Write the KVL equation for the circuit shown. 1-2 Write the KCL equation for the principal node shown. 1-2A In the DC circuit given in Fig. 1, find (i) i 1 (i) i 2 and (i) i 3.

2 1-3 Find I out and V out in the network circuit shown. 1-3A 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. 1-4 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 1-5 Find the steady state current flowing through the capacitor. 1-6 Find the input impedance of the circuit. Assume that the circuit operates at ω = 50 rad/s. o 1-6A 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. 1-7 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. 1-8 In the circuit shown, find the average power supplied by the source and the average power absorbed by the resistor.

4 1-9 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 2-1 Derive the Laplace transform for (a) u(t), (b) e -at u(t). 2-2 Obtain the Laplace transform of f ( t) 2t = δ( t) + 2u( t) 3e. 2-3 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. 2-5 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. 2-6 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 3-1 A diode has the voltage current relationship as shown. Find the current flowing through the 100Ω resistor in the two circuits using this diode. 3-2 A 741 op amp has an open-loop voltage gain of 2 x 10 5 and used in the circuit shown. Find the closed-loop gain and current i o when v s = 1V.

8 3-3 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. 3-4 For the op amp circuit shown, calculate the output voltage v o. 3-5 Calculate v o and i o in the op amp circuit shown. 3-6 Design an op amp circuit with inputs v 1 and v 2 such that v o = -5v 1 + 3v 2.

9 System Modeling 4-1 Find the electrical analogy for the mechanical system described. 4-2 Find the electrical analogy for the mechanical system described.

10 System Response 5-1 For the RC circuit shown, obtain the transfer function and its frequency response. Let v s = V m cosωt. 5-2 Determine the type of filter of the following RC circuit. 5-3 In the circuit shown, determine the type of filter (a) in stage 1, (b) in stage 2, and (c) overall.

11 Sensors 6-1 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. 6-2 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. 6-3 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 6-4 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 self-heating. 6-5 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 7-1 A stepper motor has 10 o per step and must rotate at 250rpm. What is input pulse rate (pulses per second) needed to operate? 7-2 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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