# Electrical Power, Ohm’s Law, and the Electron Volt

• Ohm’s Law postulates that current is directly proportional to an applied voltage and inversely proportional to resistance. This is expressed as:

Current = Voltage/Resistance, or I=V/R, which can be transposed to get;

V=IR

R=V/I

NB: Volts push Amps through Ohms.

• Electrical power is measured in terms of the Watt (W), with 1W being equal to work done by 1V to move 1C of electrons for 1 second (s), i.e 1W = 1VC/s. Also, 1C/s = 1A, therefore 1W=1VA. This means that power can be calculated as:

Power (P) = Voltage (V) × Current (I)

If V=IR is substituted for Voltage, then P = IR × I = I2R.

If I=V/R is substituted for Current, then P = V × V/R = V2/R.

• 1 horsepower (HP) is equal to 746 Watts.
• Work can be described as power used for a specific time period, and thus work can be calculated as:

Work = Power × Time (in seconds), which means that,

Power = Work/Time.

• The above formula shows that if 1W of power is used for 1 second, then the work done is: Work = 1W × 1s = 1W.s (or 1 Joule). The Joule (J) is the unit of measurement of work.
• In the circuit, work is done by the ordered flow of electrons, and the work done by these electrons is measured using the electron volt (eV), which can be calculated as follows:

1 Joule = 1W used for 1 second = 1VC/s × 1s = 1VC (Volt-Coulomb). Because 1C is 6.25 × 1018 electrons, then 1 Joule = 6.25 × 1018 electron-volt (eV).

• Electricity providers charge for work done using their electricity, and this is charged as Kilowatt-hours (kWh), which makes it a key unit of energy. 1 kilowatt-hour is equal to:

1 kWh = 1000 watt × 3600 seconds (or 1hour) = 3.6 × 106 Joules = 3.6 megaJoules = 3.6MJ.

• Electric shock is the sudden involuntary contraction of skeletal muscles caused by current flow through the body after a person touches a live wire hence completing a circuit. It can cause pain and severe burns if one touches a high-voltage wire. The human body has a resistance value range of 10-50 kΩ. At 9mA and 6mA for adult male and female respectively, the electric shock causes significant discomfort to cause each to release the live wire.
• Planet earth can be used as a conductor. The circuit where the earth is used to connect the load to the power source is called the earth return.
• When current flows through a resistance, power is dissipated and this leads to a drop in the EMF that is known as the voltage drop. This means that the voltage at either ends of the resistive load will have different voltage values. By derivation, Ohm’s Law reveals that resistance is directly proportional to voltage drop and inversely proportional to current. This has an application in the national grid.
• During power transmission, the power generated at the power station goes through a step-up transformer and its voltage is increased to about 330,000 volts which is then fed into the transmission lines. The transmission lines convey this high voltage electricity to substations where it is stepped down to voltage levels that can be used in homes or industries which is about 110V-220V and 415V respectively. The reason for stepping up the voltage before transmission is so as to reduce the current during power transmission which reduces the resistance, while also allowing for minimal voltage drop thus ensuring that power losses during transmission of electricity as kept at a minimum.