Question

A circuit which resonates at $1\text{ MHz}$ has Q of 100. Bandwidth between half-power point is}

• A. $10\text{ KHz}$
• B. $100\text{ KHz}$
• C. $10\text{ Hz}$
• D. $100\text{ Hz}$

Hint:

Quality factor is a dimensionless ratio that measures the sharpness of resonance.
A high $Q$ value means a narrower bandwidth and higher selectivity of the circuit.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks to find the bandwidth between the half-power points of a resonant circuit, given its resonant frequency and quality factor (Q).

Step 2: Key Formula or Approach:
The relationship between quality factor ($Q$), resonant frequency ($f_r$), and bandwidth ($BW$) is given by:
\[ Q = \frac{f_r}{BW} \]
Rearranging this formula gives:
\[ BW = \frac{f_r}{Q} \]

Step 3: Detailed Explanation:

• Resonant frequency, $f_r = 1\text{ MHz} = 1 \times 10^6\text{ Hz}$.

• Quality factor, $Q = 100$.

• Substituting these values into the bandwidth formula:
\[ BW = \frac{10^6\text{ Hz}}{100} = 10,000\text{ Hz} \]

• Converting to kilohertz (KHz):
\[ BW = 10\text{ KHz} \]

Step 4: Final Answer:
The bandwidth between half-power points is $10\text{ KHz}$, which corresponds to Option (A).