February 21, 2020
Today's Problem: Electrical Engineering
From tiny microchips and electronics to the electricity that powers our homes, electrical engineers’ work makes our fast-paced, plugged-in lives possible. This set of problems explores Ohm’s law, named after the German physicist and mathematician Georg Ohm, whose work was influential in electrical circuitry.
Ohm’s law states that current through a conductor between two points is directly proportional to the voltage across two points. Voltage (V) is measured in units of volts and is the electrical potential differ-ence between two points. Current (I) is measured in units of amperes and is the amount of electrical charge flowing through any given point. Resistance (R) is measured in ohms and is the resistance to flow of charge between two points. This is written as the mathematical equation V = IR.
The diagram above shows one resistor element. Resistors in an electrical circuit can be connected in series, parallel or series-parallel (a combination of the two arrangements).
5.1) The figure below shows an electrical circuit with three resistors connected in series – in a single line or with only one way for current flow.
When resistors are connected in series, the total resistance is the sum of the individual resistors, current is the same through all the resistors, and total voltage is the sum of the voltages across each resistor. These relationships can be described using the following formulas:
Given the known values for this series circuit in Table 5.1, calculate the missing voltages, currents, and resistances across each element and in total for the entire circuit using Ohm’s law, V = IR, and the formulas above for resistors in series.
5.2) The figure at right shows an electrical circuit with three resistors connected in parallel.
When resistors are connected in parallel the total current is split between the resistors, the voltage across each resistor is the same as the total voltage of the circuit, and the inverse of the total resistance is equal to the sum of the inverses of all the resistors. These relationships can be described using the following formulas:
Given the known values for this parallel circuit in Table 5.2, calculate the missing voltages, currents and resistances across each element and in total for the entire circuit using Ohm’s law, V = IR, and the formulas above for resistors in parallel.
5.3) Another important formula in electrical engineering is the electrical power rule. This formula can be used to calculate power dissipated, or released, by a circuit element. Each resistor in a circuit will dissipate electrical power, or heat energy, according to this formula. The electrical power rule is stated as P = VI. Power has units of Watts, which may sound familiar to you because light bulbs come in different wattages based on the power they consume.
Looking back at the completed Table 5.2 you did previously (showing resistors in parallel), which of the three resistors will release the most electrical power?
BAE Systems Engineer Spotlight: Helen Park
We’re grateful to BAE Systems, Inc., a patron sponsor of the MATHCOUNTS Foundation, for sponsoring this Future Engineers project! Engineers like Helen make the world a better place and have an impact in their communities. Learn about all of BAE Systems' spotlighted engineers.
Check Out Our Future Engineers!
The deadline to submit your answers to our Engineers Week Problems of the Day has passed. Thank you to everyone who participated! See our E-Week superstar problem solvers on our Future Engineers page!
- Everyone who solved at least 1 problem was considered a Future Engineer and received a certificate.
- Everyone who solved all 5 problems was recognized as a Future Engineer with Honors and received a certificate, plus entry into prize drawings for Future Engineer mood pencils and fanny packs.