Physics 9702/13 — May/June 2022

Background Concept

A physical quantity is something measurable that can be expressed as a number (\times) a unit (even if the unit is (1) for dimensionless quantities like strain). Examples of quantities: mass, time, charge, potential difference.

A unit is the standard used to measure a quantity, e.g. (\text{kg}) for mass, (\text{s}) for time, (\text{A}) for current, (\text{Pa}) for pressure.

Understanding the Question

You must choose the option where both items are quantities (not units). Each option contains a pair; some pairs mix a quantity with its unit.

Approach

For each option:

1. Decide whether each word names a quantity (thing you measure) or a unit (measurement standard).
2. Pick the option where both are quantities.

Step-by-Step Reasoning

• A: charge and ampere

  • Charge (Q) is a quantity.
  • Ampere (\text{A}) is a unit (of current).
  • So not both quantities.

• B: efficiency and kilogram

  • Efficiency is a quantity (often expressed as a percentage or a ratio).
  • Kilogram (\text{kg}) is a unit (of mass).
  • So not both quantities.

• C: pascal and strain

  • Pascal (\text{Pa}) is a unit (of pressure).
  • Strain (\varepsilon) is a quantity (dimensionless).
  • So not both quantities.

• D: period and potential difference

  • Period (T) is a quantity (measured in seconds).
  • Potential difference (V) is a quantity (measured in volts).
  • Both are physical quantities, so this is correct.

Key Takeaways

• A quantity is the measurable concept (e.g. charge, period, p.d.).
• A unit is the named standard (e.g. ampere, kilogram, pascal).
• Some quantities are dimensionless (e.g. strain) but are still physical quantities.

Common Mistakes

• Treating a unit name (ampere, kilogram, pascal) as if it were a quantity.
• Thinking “dimensionless” means “not a physical quantity” (strain is still a quantity).

Things to Be Careful About

• Distinguish potential difference (quantity) from volt (unit).
• Distinguish pressure (quantity) from pascal (unit).
• A unit can appear similar to a quantity in everyday language, but in physics the unit is the measurement label (A, kg, Pa, V, etc.).