A) It is possible to have mutual inductance with out self-inductance B) If the current in an inductor is doubled, the stored energy in it is quadrupled C) One can have an inductance without a resistance

Options

A. A & B are false
B. B & C are false
C. A & C are false
D. All are false

Answer

To solve the question, we need to analyze each of the three statements provided and determine their validity.

### Step 1: Analyze Statement A
**Statement A:** "It is possible to have mutual inductance without self-inductance."

- **Explanation:** Mutual inductance (M) between two coils depends on the self-inductances (L1 and L2) of each coil. The formula for mutual inductance is given by:
\[ M = K \sqrt{L_1 L_2} \]
where K is the coupling coefficient. Since mutual inductance is derived from the self-inductances of the coils, it is not possible to have mutual inductance without self-inductance. Therefore, this statement is **false**.

### Step 2: Analyze Statement B
**Statement B:** "If the current in an inductor is doubled, the stored energy in it is quadrupled."

- **Explanation:** The energy (U) stored in an inductor is given by the formula:
\[ U = \frac{1}{2} L I^2 \]
If the current (I) is doubled, we substitute 2I into the formula:
\[ U' = \frac{1}{2} L (2I)^2 = \frac{1}{2} L \cdot 4I^2 = 2L I^2 \]
This shows that the energy increases by a factor of 4 when the current is doubled. Therefore, this statement is **true**.

### Step 3: Analyze Statement C
**Statement C:** "One can have an inductance without a resistance."

- **Explanation:** Inductance is a property of a coil or circuit that opposes changes in current. However, every physical material has some resistance, even if it is very small. Therefore, it is not possible to have inductance without any resistance. Thus, this statement is **false**.

### Conclusion
- **False Statements:** A and C are false.
- **True Statement:** B is true.

### Final Answer
The false statements are A and C.

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