The output voltage (taken across the resistance) of a L C R series resonant circuit falls to half its peak value at a frequency of 200   Hz and again reaches the same value at 800   Hz . The bandwidth of this circuit is:

Step-by-step solution

V Output  = V R = i rms R = V 0 R Z = V 0 R R 2 + X L − X C 2 For peak X L = X C ⇒ V peak  = V 0 For V Output  = V 0 2 V 0 2 = V 0 R R 2 + X L - X C 2 R 2 + X L - X C 2 = 4 R 2 X L - X C = ± 3 R ω L - 1 ω C = ± 3 R ω 2 L C ∓ 3 R ω C - 1 = 0 ω = ± 3 R C ± 3 R 2 C 2 + 4 L C 2 L C ω 1 = - 3 R C + 3 R 2 C 2 + 4 L C 2 L C = 200 × 2 π ω 2 = + 3 R C + 3 R 2 C 2 + 4 L C 2 L C = 800 × 2 π ω 2 - ω 1 = 600 &#2