Voltages & Currents Intro to ECSE Analysis K. A. Connor Mobile Studio Project Center for Mobile Hands-On STEM SMART LIGHTING Engineering Research Center ECSE Department Rensselaer Polytechnic Institute Intro to ECSE Analysis

Circuit Mapping Voltages and Currents in Circuits vary something like elevation and velocity as monitored by a GPS. Example: Route Map for bicycle ride (next slide) A Circuit Diagram is like a map. Can we plot the voltage as a function of position in a circuit like we can plot elevation? What about current?

42 Mile Ride Near Madison, WI 14 November 201814 November 2018

Voltage Divider Circuit B C Voltage vs Position How does this differ from elevation? What happens in the battery? D E Vo A F Vo Volts G B H I K J A B C D E F G H I J K B A 14 November 201814 November 2018

What About Current? If there was a direct analogy between voltage & elevation and current and velocity, the current should increase as it flows down hill. Current is not one or a few charges moving around a circuit, it is an immense number filling the circuit and all moving at once, at a constant velocity. 14 November 201814 November 2018

Voltage Divider With Load Where is the voltage equal to Vin? Where is it equal to Vout? Where is it equal to zero? Is the current the same everywhere? Is the current from the source the same with and without the load resistor RL? 14 November 201814 November 2018

What Did We Learn? There is a specific voltage everywhere in the circuit but we may not be able to determine it inside of a device. Voltage drops monotonically from one end of the source to the other. Note, we have only considered DC voltages. Current is the same everywhere along a series path. It does not change with voltage. 14 November 201814 November 2018

Voltage Divider With Load What is the power generated by Vin? What is the power dissipated in R2, R1 & RL? Why is this circuit a bad idea? When does it work well? 14 November 201814 November 2018

Voltage Divider With Load We need a way to use the voltage divider without changing the way it works This requires that we divert essentially no current from it We will see how to do this with an operational amplifier 14 November 201814 November 2018