Harold Hall
Had different values of R1 and R2 been chosen so as to take a higher current, say R2 taking 2 amp at 3 volts the results would have been different. The increase in current (0.5 to 0.6 amps) through the motor would result in the current through R1 increasing from 2.5 to 2.6 amps. The volt drop across R1 would again increase proportionately but this time only from 9 volts to 9.36 volts (9 x 2.6/2.5). The motor voltage, and speed, would as a result reduce less. From this it can be seen that the greater the current passing through the potential divider the less its output is affected by changes in the load placed on it.
I must though clarify that the above is an over simplification as the decrease in voltage at the motor is also apparent at the resistor R2 the current through this will therefor drop, compensating in part for the increase in motor current, the changes in motor voltage are therefor less than suggested. However, whilst mathematically not totally correct, the principle it attempts to explain is still valid, the greater the current through the divider compared to the load the more stable is the output.
Actually, the motor voltage falls from 3 volts to 2.6 V in the first instance and with the higher current through R2, to only 2.9 V. The principle would of course be equally appropriate to a potential divider feeding any form of varying load, not just a motor. I have left out the formula for calculating these values to avoid over complication.
This suggested method of motor speed control would have been used in the pre electronic era, even for quite large motors, it should be obvious though that it is very inefficient in terms of power consumption as the divider uses even more power than the motor itself.
Metalworking
Workshop Data
Its use in the application used for my explanation may just be valid for the workshop owner who does not want to delve into electronic systems. In this case the potential divider could be made using more than two resistors giving more than the two speeds suggested.
The main purpose of the explanation is to highlight the fact that when setting up a potential divider, the actual value of the resistors can be almost as important as the ratio between them. I chose the case of a motor with a varying load as I felt this would be better understood, it is though equally applicable to dividers in electronic circuits. In this case though, with the load current often being in micro amps the current through the divider can be proportionately much higher and the effect of load change almost nil.
Voltages in a loop
Understanding the effect of current and resistance on the voltages in a loop is essential to the understanding of electrical circuits. Rather like the law mentioned above for currents arriving and leaving a point in a circuit, Kirchoff also provided another law for the voltages in a loop. This though is a little more complex to understand and so my version states that the sum of the voltages in a loop is always zero.
Sketch 9 shows that the current resulting from the applied voltage, Vin, produces
voltages of V1 and V2 across resistors R1 and R2. Also, it can be seen that the polarity
of the voltages V1 and V2 are in the opposite direction to Vin. Therefor, the sum
total of the voltages in the loop equals zero, that is, Vin-
