Which one of the following doesn't have a derived unit?

Options

A. Frequency
B. Planck's constant
C. Electric current
D. Charge

Answer

To determine which of the following options does not have a derived unit, we will analyze each option and identify whether it is a derived unit or a fundamental unit.

### Step-by-Step Solution:

1. **Understanding Derived and Fundamental Units**:
- Derived units are those that can be expressed in terms of fundamental units. For example, velocity (m/s) is a derived unit because it is derived from the fundamental units of length (meters) and time (seconds).
- Fundamental units are the basic units of measurement that cannot be derived from other units. Examples include meter (length), kilogram (mass), second (time), and ampere (electric current).

2. **Analyzing the Options**:
- **Option 1: Frequency**:
- Frequency (measured in hertz, Hz) is defined as the number of occurrences of a repeating event per unit time. It can be derived from the fundamental unit of time (seconds). Therefore, frequency is a derived unit.

- **Option 2: Planck's Constant**:
- Planck's constant (h) has units of energy multiplied by time (Joule-seconds). Since Joules can be expressed in terms of fundamental units (kg·m²/s²), Planck's constant is also a derived unit.

- **Option 3: Electric Current**:
- Electric current is measured in amperes (A). The ampere is a fundamental unit of measurement in the International System of Units (SI). It cannot be derived from other units, making it a fundamental unit.

- **Option 4: Charge**:
- Electric charge (measured in coulombs) is derived from the fundamental unit of current (amperes) and time (seconds). Therefore, charge is a derived unit.

3. **Conclusion**:
- After analyzing all the options, we find that electric current (Option 3) is the only quantity that does not have a derived unit. It is a fundamental unit.

### Final Answer:
The option that does not have a derived unit is **Option 3: Electric Current**.