An LED is very efficient because within the LED itself, the electrical energy is directly converted to light. This energy transfer happens one electron at a time: each electron that crosses the LED loses the same amount of energy by emitting a a photon whose energy (in eV) is hc/A, where hc = 1240eVnm and A is the wavelength of the light, in nm. The change in the electron's electrical energy is, of course, U = eV where e is the electron charge and V the voltage across the LED. When the LED is on it will therefore have a constant voltage in Volts VLED = hc/(ex) = 1240/A across it, where A is the wavelength in nanometers. If no current flows, i.e. if the voltage would be less than VLED, the LED is off and acts like an open switch and has whatever lower voltage is consistent with the rest of the circuit. Consider a circuit with an ideal 3V battery, a resistor and an LED in series. We'd like to use the circuit to light LED's ranging in color from the infrared (wavelength of 1100 nm) to the near UV (about 350 nm.) The symbol for an LED is The circuit looks like this: The (conventional) current would flow from left to right in the LED shown here. The same rules for voltage (the voltages add) and current (it's the same in both components) in series circuits apply here, as they do in all series combinations regardless of the components that are involved. (a) Using the circuit diagram, write the voltage equation. (b) Calculate the LED voltages across a lit LED for the shortest (350 nm) and longest (1100 nm) wavelengths I wish to use. To actually turn a given LED on, my battery voltage needs to be at least as large as the voltage you calculated for that LED. Will I be able to use this circuit with a 3V battery to light the LED's over the entire desired wavelength range? If not, what is the range of wavelengths that I can use it for? (c) The resistor is there to protect the LED, which will burn out if the current exceeds 0.10 A. What will be the largest resistor voltage in the circuit as I vary the LED wavelength over the range I specified? Using the result you just found, find the minimum value of the resistor needed so that the current never exceeds 0.10 A for any of the colors we are interested in. (I am looking for one value of resistance that will work regardless of the LED I choose! See the homework guide for hints.) (d) Look up wavelength for blue light as well. What is the current in the circuit, using the resistance you just calculated for the resistor, when it is used with a 1240 nm IR LED? an 1100 nm IR LED? a red LED? blue LED? a UV, 350 nm, LED? (e) What are the power provided by the battery, the power dissipated in the resistor, and the power converted to light in the LED for the LEDs considered above?