A radio tuning circuit contains a series LCR combination. To tune into a station broadcasting at a frequency of 10^6 2 Hz, the circuit must resonate at this frequency. If the circuit has a fixed inductor of 100 H, what should be the capacitance of the variable capacitor?

Step-by-step solution

The resonant frequency of a series LCR circuit is given by f_r = 1 2 LC . Squaring both sides and rearranging for capacitance C gives: C = 1 4 ^2 f_r^2 L Given f_r = 10^6 2 Hz and L = 100 H = 10⁻⁴ H. Substituting the values: C = 1 4 ^2 ( 10^6 2 )^2 10⁻⁴ C = 1 4 ^2 ( 10¹² 4 ^2 ) 10⁻⁴ C = 1 10¹² 10⁻⁴ = 1 10^8 F C = 10⁻⁸ F = 10 nF Answer: 10 nF