The variable capacitor in the tuner of an AM radio has a capacitance of 1150 pF when the radio is tuned to a station at 690 kHz.
What must be the capacitance for a station at 1500 kHz? What is the inductance (assume constant)? Ignore resistance.
What must be the capacitance for a station at 1500 kHz? What is the inductance (assume constant)? Ignore resistance.
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w^2 = 1/LC
w1 = 2pi*690 kHz = 4.335e6 rad/s
w1^2 = 1.880e13
w2^2*C2 = w1^2*C1
C2 = C1*(w1/w2)^2 = 1150 pF*(690/1150)^2 = 414 pF
L = 1/(1.88e13*1150e-12) = 46.25uH
w1 = 2pi*690 kHz = 4.335e6 rad/s
w1^2 = 1.880e13
w2^2*C2 = w1^2*C1
C2 = C1*(w1/w2)^2 = 1150 pF*(690/1150)^2 = 414 pF
L = 1/(1.88e13*1150e-12) = 46.25uH