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: Define the Quality Factor (Q).The quality factor (Q) of a resonant circuit indicates its selectivity. It's the ratio of the resonant frequency (\(f_0\)) to the bandwidth (BW).\[ Q = \frac{f_0}{BW} \]
Step 2: State the known values.We have: \(f_0 = 1 \text{ MHz} = 1,000,000 \text{ Hz}\) and \(Q = 10\).
Step 3: Determine the bandwidth.Using the formula, \( BW = \frac{f_0}{Q} \), substitute the known values:\[ BW = \frac{1,000,000 \text{ Hz}}{10} = 100,000 \text{ Hz} \]Therefore, the bandwidth is:\[ 100,000 \text{ Hz} = 100 \text{ kHz} \]