Question

When you ask why they are late with their share of the rent (again), your roommate explains that they would like to invest the money into buying inexpensive force sensors for about $10 each. They think they can use these to make cheap electronic drum kits and sell them at a profit. The idea is to connect a force sensor acting as a switch between a 9 V battery and an old 50 Ω (load resistance) speaker. Each customer will supply their own battery and speaker, and the wire will be pilfered. While perusing the specs for the force sensor, you notice that they have a typical source resistance of about 100 kΩ. Model the proposal as a DC voltage divider, which is sufficient analysis to see what a terrible design your roommate has concocted. What’s the maximum voltage you would see across the speaker given the source resistance and load resistance? What’s the maximum power that would be consumed by the speaker? Compare this with the power consumed by the speaker at typical operating voltages of at least 1 V.

Answer 1

Answer

The current in a series circuit consisting of 9V battery, the force sensor (of source resistance 100Kohm) and 50ohm speaker will be

I_speaker = 9/(100000+50) amps

I_speaker = 89.9 microamps

This current will not be sufficient to drive the speaker.

The other way to look at the same scenario is to find out the voltage across the speaker. Using the potential divider formula the voltage across the speaker turns out to be:

V_speaker = 9 * 50/(100000+50)

V_speaker = 4.5mV

Again this is not sufficient to drive the speaker.

Compare this with the situation when 1V source is connected directly across the speaker:

In this case the current would be

I_speaker = 1/50 = 20mA

This is considerably higher than the current when force sensor was place between the battery and the speaker.