Answer:
a
[tex]C_{max} = 63.3 n F[/tex]
b
[tex]C_{min} = 6.182 nF [/tex]
Explanation:
From the question we are told that
The minimum frequency is [tex]f_{min} = 500kHz = 500*10^{3} \ Hz[/tex]
The maximum frequency is [tex]f_{max} = 1600 kHz = 1600*10^{3} \ Hz[/tex]
The inductance is [tex]L = 1.6 \mu H = 1.60 *10^{-6} \ H[/tex]
Generally the low band frequency is mathematically represented as
[tex]f_{min} = \frac{1}{2\pi \sqrt{LC_{max}} }[/tex]
=> [tex]C_{max} = \frac{1}{4 \pi^2 * f_{min}^2 * L }[/tex]
=> [tex]C_{max} = \frac{1}{4 * 3.142 ^2 * 500*10^{3} * 1.60 *10^{-6} }[/tex]
=> [tex]C_{max} = 6.33 * 10^{-8} \ F[/tex]
=> [tex]C_{max} = 63.3 n F[/tex]
Generally the high band frequency is mathematically represented as
[tex]f_{max} = \frac{1}{2\pi \sqrt{LC_{min}} }[/tex]
=> [tex]C_{min} = \frac{1}{4 \pi^2 * f_{max}^2 * L }[/tex]
=> [tex]C_{min} = \frac{1}{4 * 3.142^2 * ( 1600*10^{3})^2 * 1.60 *10^{-6} }[/tex]
=> [tex]C_{min} = \frac{1}{4 * 3.142^2 * ( 1600*10^{3})^2 * 1.60 *10^{-6} }[/tex]
=> [tex]C_{min} = 6.182 *10^{-9} \ m [/tex]
=> [tex]C_{min} = 6.182 nF [/tex]
