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Homework set 6 – due date: Wednesday, November 15, 2017
1. When measured with open circuit (no load – zero current draw) the terminals of a battery show a voltage
of 13.6 volts. When delivering 10. amps to an external load, the voltage drops to 11.2 volts. What is the
value of the constant voltage source (Vs) and the internal resistance (Rs)? (hint: draw circuit, use KVL &
Ohm’s law)
2. An automobile battery is modeled as a 12V ideal voltage source in series with a 0.3 Ohm internal
resistance. It is to be charged from a 15 V source (the alternator). The charging current must be limited
to 2.0 Amps by placing a resistor in series with the 15 volt source. What resistance will achieve the
desired current? (Note when charging a battery the “larger” source must drive current into the battery.)
3. The circuit shown to the right contains a constant voltage source (Vs = 24V), 3 resistors and a capacitor.
Voltage is zero at point A.
a. Using Ohm’s law, write expressions for I1, I2, and I3 as a function of the voltages VC (variable)
and Vs (constant), as well as resistances. Note that the voltage at point A is zero.
b. Now consider the system after it has reached steady-state. Determine the currents I1, I2, I3 and I4.
c. At steady-state, what is the voltage at points B and C if the voltage at point A is zero? What is the
charge (Coulombs) on the capacitor?
d. The switch is opened, removing the voltage source from the circuit. Sketch (don’t calculate
points) Vc and I4 vs time as the capacitor discharges.
4. An electric motor drives an air compressor that delivers air with inlet and outlet conditions as
shown on the figure. The motor-compressor set operates at steady-state conditions. Experience
shows that changes in kinetic and potential energy are negligible for this system. If the
volumetric flow rate of the air at inlet (point 1) is 0.185 m3/s and the measured heat transfer rate
from the compressor is 20.0 kilowatts, what is the electric power needed to be supplied to the
motor (at 380 volts A.C.)? Assuming the motor efficiency is 85%.
P1=1 atmg, T1 = 310 K
H1=305 kJ/kg
380 V AC
Electric Motor
Compressor
P2=8 atmg, T2 = 500 K
H2=501 kJ/kg
…
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