Which of the following is a vector quantity?

Options

A. Current density
B. Current
C. Wattless current
D. Power

Answer

To determine which of the following is a vector quantity among the options provided (current density, current, wattless current, and power), we can analyze each option step by step.

### Step 1: Analyze Current Density
- **Definition**: Current density (J) is defined as the current (I) flowing per unit area (A), mathematically expressed as \( J = \frac{I}{A} \).
- **Vector Nature**: Current density can also be expressed as the product of charge density (ρ) and velocity (v), \( J = ρv \). Since velocity is a vector quantity, current density is also a vector quantity.

**Conclusion**: Current density is a vector quantity.

### Step 2: Analyze Current
- **Definition**: Current (I) is the flow of electric charge and is measured in amperes (A).
- **Scalar Nature**: Current is a scalar quantity because when multiple currents meet at a junction, they combine as an algebraic sum, not as a vector sum.

**Conclusion**: Current is a scalar quantity.

### Step 3: Analyze Wattless Current
- **Definition**: Wattless current refers to the component of current that does not contribute to power consumption, often seen in AC circuits.
- **Scalar Nature**: Since wattless current is essentially a type of current, it retains the properties of current and is also a scalar quantity.

**Conclusion**: Wattless current is a scalar quantity.

### Step 4: Analyze Power
- **Definition**: Power (P) is defined as the rate at which work is done or energy is transferred, given by the formula \( P = \frac{W}{t} \), where W is work and t is time.
- **Scalar Nature**: Both work and time are scalar quantities, hence power, being the ratio of two scalars, is also a scalar quantity.

**Conclusion**: Power is a scalar quantity.

### Final Conclusion
From the analysis:
- Current density is a vector quantity.
- Current, wattless current, and power are scalar quantities.

Thus, the answer to the question "Which of the following is a vector quantity?" is **current density**.

---