# E72 (P)review

### Problem 1.

 For the circuit shown all resistors are 1kΩ. Find the equivalent resitstance between terminals A and B. Between C and D. Between B and C. ### Problem 2.

 For the circuit shown: Find the Thevenin equivalent between nodes B and C. Do it once without using superposition, and once with it. Find the Thevenin equivalent between nodes A and C. Use any method ### Problem 3.

 For the circuit shown (note this is case 3 of the Thevenin Theorem): Find the Thevenin equivalent between nodes A and B. Between C and D. ### Problem 4.

 For the circuit shown: Find Rx such that the power dissipated through it is maximized (hint: find the Thevenin equivalent circuit experienced by Rx and use maximum power transfer) With the value of Rx chosen, find the power dissipated in Rx, and the total power dissipated in the other resistors. ### Problem 5.

 For each circuit find the voltage, v(t), at the output terminals if: the input has been zero volts for a long time, and then goes to 1 volt. the input has been 1 volt for a long time, and then goes to -1 volt. The resistor has value=R, and the capacitor has value=C. ### Problem 6.

 For the two circuits of the previous problem, with  R=1kΩ, C=1uF: Construct the Bode plots. From the Bode plots determine the output voltage if the input is 10sin(100t). Determine the output voltage if the input is 10sin(10000t). What type of filtering operation does each circuit perform?

### Problem 7.

 For the circuit shown find vx(t) if: the switch has been closed for a long time, and is opened at t=0. the switch has been open a long time and is closed at t=0. R1=R2=R3=1kΩ, C=1uF. ### Problem 8.

 Solve for the two cases given. The voltage across the capacitor is 1/3 V1 at t=0 when the switch opens.  Solve for the time at which the voltage across the capacitor is 2/3 V1. The voltage across the capacitor is 2/3 V1 at t=0 when the switch closes.  Solve for the time at which the voltage across the capacitor is 1/3 V1 if at t=0: ### Problem 9.

 For the circuit shown The capacitor is charged to 2.2 V when the switch is closed at t=0,.  Calculate how long it takes the voltage across the capacitor to go from 2.2V (at t=0) to 1.4V. The capacitor is charged to1.4 V when the switch is opened at t=0.  Calculate how long it takes the voltage across the capacitor to go from 1.4V (at t=0) to 2.2V.  Since R5 is so much less than the other resistances in the circuit, assume it has a value of 0 for this part of the problem. (extra - you need not do this) Repeat the previous part without assuming R5=0Ω. ### Problem 10.

 If the voltage (or any other quantity) in a first order system starts at v(0+) and ends at v(∞), show that the time time, t1, at which it reaches the voltage v1 (i.e., v(t1)=v1) is given by: ### Problem 11.

 For the circuit shown: What type of filter is this?  Make your argument without equations, based upon the low and high frequency behavior of the circuit elements. Find the transfer function (Vo(s)/Vi(s)) Verify that your transfer function agrees with part a. Does the damping factor increase or decrease as R increases? ### Problem 12.

 For the circuit shown: What type of filter is this?  Make your argument without equations, based upon the low and high frequency behavior of the circuit elements. Find the transfer function (Vo(s)/Vi(s)) Verify that your transfer function agrees with part a. Does the damping factor increase or decrease as R increases? ### Problem 13.

 The circuit shown is a Wheatstone bridge, and is often use to measure small changes in resistance (denoted by the lowercase "r"). Show that when r=0, Vo=0. Derive an expression for Vo in terms of Vi, R, and r. If r<

### Problem 14.

 For the circuit shown: Find the voltage between B and C using superposition. Find the voltage between A and C. ### Problem 15.

 The resistor network shown repeats forever to the right.  What is the equivalent seen between A and B?  All resistors are equal with resistance R. Hint: The resistance to the right of A/B is the same as the resistance to the right of C/D. ### Problem 16.

 Most newer electronic products say they are ROHS compliant.  What does this mean and why is ROHS compliance important environmentally?  Why is it important for a company's product to be ROHS compliant?