Question

A circuit which resonates at 1 MHz has a Q of 10. Bandwidth between half-power points is

• A. 1 kHz
• B. 10 kHz
• C. 100 kHz
• D. 100 Hz

Hint:

The relationship \(Q = f_0 / BW\) is fundamental for any resonant system. A high Q means a narrow bandwidth (high selectivity), while a low Q means a wide bandwidth (low selectivity).

Answer 1

The Correct Option is C

Step 1: Recall the definition of the Quality Factor (Q). The quality factor of a resonant circuit is a measure of its selectivity. It is defined as the ratio of the resonant frequency (\(f_0\)) to the bandwidth (BW). \[ Q = \frac{f_0}{BW} \]
Step 2: Identify the given values. Resonant frequency, \(f_0 = 1 \text{ MHz} = 1,000,000 \text{ Hz}\). Quality factor, \(Q = 10\).
Step 3: Calculate the bandwidth. Rearrange the formula to solve for BW: \[ BW = \frac{f_0}{Q} \] Substitute the given values: \[ BW = \frac{1,000,000 \text{ Hz}}{10} = 100,000 \text{ Hz} \] Convert the result to kilohertz: \[ 100,000 \text{ Hz} = 100 \text{ kHz} \]