Voltage Dividers

For "voltage dividers," we are attempting to control the voltage in a circuit such that it hovers between an upper and lower bound. To control this, we can adjust the total resistance in the circuit. We have a constant shunt resistor, and a batch of 3 resistors on a bus which can be put in parallel to lower the equivalent resistance. Through calculations, I determined that Req max (one resistor on) corresponds to the maximum voltage across the bus, and that Req min (all 3 resistors in parallel) corresponds to the minimum voltage. After solving a system of equations, I found that our constant shunt resistor should be 55.47 ohms and that our constant voltage source should run at 5.54 volts. Using Kirchoff's laws, our group could determine that the resulting "max" and "min" bus currents were .00525A and .01425A, respectively.

Next, we actually tested our setup. We had to use slightly different values in practice because our equipment couldn't mimic the ideal calculated values.

Here is the data:

1 load

Req = 1000ohms; Vbus = 5.72V; Ibus = 0.00581A

2 loads

Req = 500ohms; Vbus = 5.43V; Ibus = 0.01096A

3 loads

Req = 332.6ohms; Vbus = 5.18V; Ibus = 0.01559A

Finally, we worked out the actual % variation in voltage, which was very high (14%). Again, this was due to the fact that our resistor box didn't correspond to the calculated shunt resistor value that would yield a perfect 5% variation.

The last problem involved the sort-of inverse of our original situation: if the equivalent resistance was kept constant, how would we have to vary the shunt resistor in order to create a 1% variation in bus voltage? Using a similar system of equations, I found that Rs = 32.24 ohms yielded the upper bound and Rs = 39.73 ohms yielded the lower.