Assertion : Kilovol-ampere (kVA) and kilowatt-hour have the same dimensions.
Reason : Both are the units of energy.

Options

A. If both Assertion and Reason are true and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are true and Reason is not correct explanation of Assertion.
C. If Assertion is true but Reason is false.
D. If both Assertion and Reason are false.

Answer

To solve the question, we need to analyze the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states that "Kilovolt-ampere (kVA) and kilowatt-hour (kWh) have the same dimensions."

- **Kilovolt-ampere (kVA)** is a unit of apparent power in an electrical circuit.
- The dimensions of power can be expressed as:
\[ \text{Power (P)} = \text{Voltage (V)} \times \text{Current (I)} \]
The unit of power is Volt-Ampere (VA), and thus:
\[ \text{Dimensions of kVA} = [M^1 L^2 T^{-3}] \text{ (since V = M L^2 T^{-3} I^{-1})} \]

### Step 2: Understand the Reason
The reason states that "Both are the units of energy."

- **Kilowatt-hour (kWh)** is a unit of energy. It is defined as the amount of energy consumed when a power of one kilowatt is used for one hour.
- The dimensions of energy can be expressed as:
\[ \text{Energy (E)} = \text{Power (P)} \times \text{Time (t)} \]
Since the unit of power is kilowatt (kW), and time is in hours (h), the dimensions of energy become:
\[ \text{Dimensions of kWh} = [M^1 L^2 T^{-2}] \text{ (since kW = M L^2 T^{-3})} \]

### Step 3: Compare Dimensions
Now, we compare the dimensions of kVA and kWh:

- Dimensions of kVA: \([M^1 L^2 T^{-3}]\)
- Dimensions of kWh: \([M^1 L^2 T^{-2}]\)

Since the dimensions are not the same, the assertion is **false**.

### Step 4: Evaluate the Reason
The reason states that both units are units of energy. Since kVA is a unit of power and kWh is a unit of energy, this statement is also **false**.

### Conclusion
Both the assertion and the reason are false. Therefore, the correct answer is that both the assertion and the reason are false.

### Final Answer
Both assertion and reason are false.

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