The transistor in the circuit has parameters $K_p=$ $0.5 \mathrm{~mA} / \mathrm{V}^2, V_{T P}=-2 \mathrm{~V}$, and $\lambda=0$. (a) Determine $R_o$. (b) What is the expression for the circuit time constant? (c) Determine $C_C$ such that the lower $3 \mathrm{~dB}$ frequency is $20 \mathrm{~Hz}$.

(a) A Mealy sequential circuit has one input (x) and one output (z). z = 1 if and only if the most recent input, combined with the preceding three inputs, was not a valid BCD encoding of a decimal digit; otherwise, z = 0. Assume the BCD digits are received most significant bit first. Derive a state table for the circuit. (Seven states are sufficient.) (b) Repeat for a Moore circuit (i.e., z = 1 if and only if the previous four inputs were not a valid BCD digit). (Thirteen states are sufficient.) (c) Is it possible for a Moore circuit to generate the correct output while the fourth input bit is present rather than after it has been received? Explain your answer.

When making an ECG measurement, it is important to measure voltage variations over small time intervals. The time is limited by the RC constant of the circuit-it is not possible to measure time variations shorter than RC. How would you manipulate R and C in the circuit to allow the necessary measurements?

Over a period of $5 \mathrm{~min}, 7,500 \mathrm{C}$ is found to have traveled past a particular point in a circuit. How much current must have been flowing through the circuit? A. $25 \mathrm{~A}$ C. $7,500 \mathrm{~V}$ B. $1,500 \mathrm{~V}$ D. $37,500 \mathrm{~A}$

A capacitor that is initially uncharged is connected in series with a resistor and a $400.0 \mathrm{~V}$ emf source with negligible internal resistance. Just after the circuit is completed, the current through the resistor is $0.800 \mathrm{~mA}$ and the time constant for the circuit is $6.00 \mathrm{~s}$. What are
(a) the resistance of the resistor
(b) the capacitance of the capacitor?

The equivalent impedance, $Z_\text{EQ}$, of an $LC$ tank circuit measures $150\text{ k}\Omega$ using the experimental technique shown in Fig. 25–9. If the resonant frequency is $2.5\text{ MHz}$ and $L=50\space\mu\text{H}$, calculate the $Q$ of the resonant circuit.

A common-emitter equivalent circuit is mentioned here. (a) What is the expression for the Miller capacitance? (b) Derive the expression for the voltage gain $A_v(s)=V_o(s) / V_i(s)$ in terms of the Miller capacitance and other circuit parameters. (c) What is the expression for the upper $3 \mathrm{~dB}$ frequency?

Compare the delay in sending an x-bit message over a k-hop path in a circuit-switched network and in a (lightly loaded) packet-switched network. The circuit setup time is s sec, the propagation delay is d sec per hop, the packet size is p bits, and the data rate is b bps. Under what conditions does the packet network have a lower delay? Also, explain the conditions under which a packet-switched network is preferable to a circuit switched network.

The armature, frame, and core of a 12-VDC control relay are made of sheet steel. The average length of the magnetic circuit is $12 \mathrm{~cm}$ when the relay is energized, and the average cross section of the magnetic circuit is $0.60 \mathrm{~cm}^2$. The coil is wound with 250 turns and carries $50 \mathrm{~mA}$. Determine: a. The flux density $\mathcal{B}$ in the magnetic circuit of the relay when the coil is energized. b. The force $\mathcal{F}$ exerted on the armature to close it when the coil is energized.

Graph models of the sidewalks in two sections of a town are shown below. Parking meters are placed along these sidewalks.

a. Why would it be helpful for a parking-control officer to know if these graphs have Euler circuits?

b. Does the graph that models the east section of town have an Euler circuit? Explain your reasoning.

c. Does the graph that models the west section of town have an Euler circuit? Does it have more than one Euler circuit? Explain.

Data Analysis The table shows the numbers $a_n$ of Circuit City stores for the years $1991$ to $2000.$

Which model do you think would better predict the number of Circuit City stores in the future? Use the model you chose to predict the number of Circuit City stores in $2005.$

According to its design specification, the timer circuit delaying the closing of an elevator door is to have a capacitance of 32.0 $\mu F$ between two points A and B. When one circuit is being constructed, the inexpensive but durable capacitor installed between these two points is found to have capacitance 34.8 $\mu F$. To meet the specification, one additional capacitor can be placed between the two points. (a) Should it be in series or in parallel with the 34.8-$\mu F$ capacitor? (b) What should be its capacitance? (c) What If ? The next circuit comes down the assembly line with capacitance 29.8 $\mu F$ between A and B. To meet the specification, what additional capacitor should be installed in series or in parallel in that circuit?

A parallel RL circuit has $R=4 \Omega$ and L = 1 H. The input to the circuit is $i_{s}(t)=1.4 e^{-t} u(t)$ A. Find the inductor current $i_{L}(t)$ for all t > 0 and assume that $i_{L}(0)=-1.4 \mathrm{A}$.

A PMOS version of the current-source circuit is mentioned here. The transistor $M_2$ sources a bias current to a load circuit. Assume the circuit is biased at $V^{+}=+5 \mathrm{~V}$ and $V^{-}=-5 \mathrm{~V}$, and assume the transistor parameters are $V_{T P}=-0.5 \mathrm{~V}, k_p^{\prime}=50 \mu \mathrm{A} / \mathrm{V}^2,(W / L)_1=$ $(W / L)_2=15,(W / L)_3=3$, and $\lambda=0$. Determine $I_{\mathrm{REF}}, I_O$, and $V_{S D 2}$ (sat).