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?

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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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/λ, where
hc = 1240eV nm and λ 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/(eλ) = 1240/λ across it,
where λ 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?

(f) Consider the power at very long wavelengths and at very short wavelengths. Why is there a
wavelength at which the LED's power output in this circuit is maximum? (By the way, this is
also why solar cells, which operate on the same principle but in reverse, have a limit on their
efficiency!)

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