Final Exam (BMEN-321)
NOTES: 1) There are problems on BOTH the front and back pages of the exam. 2) You need to show
ALL the work done and not just answers in order to get full credit.
1) Two batteries rated at 1 ampere-hour with a nominal voltage of 1.5 V are connected in series to supply
energy to a flashlight. The flashlight lamp has a resistance of 5 Ω. When the flashlight is on, the voltage across
the lamp is 2.5 V. How many hours of use would the battery supply? (15 pts)
2) In the circuit below, determine the power dissipated by the 4 Ω resistor. (15 pts) 3) In the circuit below: a) Derive the expression for the output voltage Vout in terms of the input current Iin. (10 pts)
b) Assuming that R=R1=R2=1000 ohms, and the power supplies of the op-amp at 10 V and -10V, sketch the
output voltage if the input current is Iin (t) = 4cos(20Ï€t) mA. (5 pts)
4) A transducer output signal has a bandwidth of 30 Hz and spans in the range of -200 to 200 mV.
a) Design a circuit that will condition the filtered signal, so that it can be applied to the input of an Analog-toDigital Converter (ADC) that accepts voltage signals in the range of 0-5 V. Specify the value for each of
the circuit components and voltage levels. (15 pts)
b) Select the sampling frequency of the ADC and the number of bits if you want an amplitude resolution of 5
mV. (5 pts)
5) Design a resistor attenuator to make ! = ! /1000 using the circuit configuration below. This problem is
under-constrained and has many possible answers. (10 pts) 8) The circuit shown below is widely used in the design of audio equalizers. For the given circuit, derive the
transfer function: = !!"# (!)
!!" (!) and plot the magnitude and the phase responses. (10 pts) Wires do not touch each other here. 6) One of the most common industrial applications of strain gauges is in the design of a pillar load cell shown in
the figure below (on the left). A pillar load cell consists of 4 strain gauges mounted on a metallic post, such that
two strain gauges measure the longitudinal strain (strain gauges 2 and 4 in the figure below) and the remaining
two strain gauges measure the transverse strain (strain gauges 1 and 3 in the figure below). To measure a
force (F), the strain gauges are connected in a Wheatstone bridge configuration shown on the right in the
figure below, where the strain gauges are represented as resistances (R1 corresponds to strain gauge 1, R2
corresponds to strain gauge 2; R3 corresponds to strain gauge 3, and R4 corresponds to strain gauge 4).
Assuming:
Unstrained resistance = R (for all strain gauges)
Gauge factor = G (for all strain gauges)
Cross-sectional area of the metallic post = A
Young’s Modulus of the metallic post = Y
Poisson’s ratio of the metallic post = Input Voltage of the Wheatstone bridge = Vs
Obtain an expression for the applied force F in terms of the output voltage V0 and the variables defined above.
(15 pts) + _
_ + _
_ Figure Source: Bentley, 4e, Pearson

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