Units and Measurement

The charge-to-mass ratio (e/m) of an electron has units of coulombs per kilogram (C/kg) since it is obtained by dividing the charge in coulombs by the mass in kilograms. J.J. Thomson measured this ratio to be approximately 1.76 × 10^11 C/kg. This specific ratio helped identify the electron as a fundamental particle. Option B correctly represents the unit as C/kg. Options A and D are incorrect units, while e/m is not dimensionless.

Watt-hour measures energy consumed or produced over time. It is calculated by multiplying power (in watts) by time (in hours), making it a unit of energy, not power or instantaneous quantities.

Tesla (T) is the SI unit of magnetic flux density, defined as one weber per square meter (Wb/m²). Gauss is a CGS unit, Oersted measures magnetic field strength, and Weber measures magnetic flux.

Impedance is the total opposition to AC current flow, combining resistance and reactance. Like resistance and reactance, impedance is measured in ohms.

Joule is the unit of energy, work, and heat in the International System of Units (SI). It measures the energy transferred when a force of one newton moves an object one meter. Heat is a form of energy, so saying joule is the unit of heat is also correct.

1 Joule is equal to 10^7 ergs in the CGS (centimeter-gram-second) system. This conversion is fundamental in physics when working between different unit systems. The Joule is the SI unit of energy, while the erg is the CGS unit.

The unit of electric current is the Ampere (A), named after French physicist André-Marie Ampère. Ohm measures resistance, Watt measures power, and Volt measures potential difference. Current is the flow of electric charge through a conductor.

In the MKS (meter-kilogram-second) system, the unit of energy is the Joule. The MKS system is the basis for the modern SI system. Volt is potential difference, Erg is energy in the CGS system, and Ohm is resistance.

The unit of capacitance is the Farad (F), not the Henry. The Henry (H) is the unit of inductance, which measures opposition to changes in current. Capacitance measures a capacitor's ability to store charge per unit voltage.

Angstrom (Å) is a unit of length equal to 10⁻¹⁰ meters, commonly used to measure atomic and molecular distances, wavelengths of light, and sizes of microscopic structures. It is not used for weight, mass, or time.

Joule is the SI unit of energy. Calorie is a unit of thermal energy commonly used in nutrition. Kilowatt-hour is a unit of energy used for electricity billing (equal to 3.6 megajoules). Watt, however, is a unit of power (rate of energy use), not energy itself.

All four are valid angle units. Radian and degree are the most common, with 2π radians = 360 degrees. Minute (1/60 degree) and second (1/60 minute = 1/3600 degree) are subdivisions used for precise measurements in navigation and astronomy.

The series follows metric prefixes in increasing order of magnitude: attometer (10^-18), femtometer/fermi (10^-15), picometer (10^-12). The next logical step in the standard SI sequence (increasing by factors of 10^3) is nanometer (10^-9).

Kilowatt (kW) is the odd one out because it's a unit of POWER (rate of energy use), while joule, calorie, and kilowatt-hour are all units of ENERGY or work done. Power = Energy / Time, so 1 kW = 1 kJ/s. The kilowatt-hour (kWh) is a unit of energy equal to 1 kW used for 1 hour.