Question

1. Radios often utilize a variable capacitor (capacitance is changed by either changing the distance between plates or amount of dielectric between plates) in series with an inductor to tune the circuit to a particular frequency. In a particular shortwave radio, the value of the inductor is \(L=1.09 \mu H .\) What must be the capacitance (in \(\mathrm{pF}\) ) of the circuit so that the radio is tuned to a frequency of \(\mathrm{f}=6.95 \mathrm{MHz}\) ?

2. A conducting coil, with current \(i(t)=4.20 * e^{0.0250 t} \sin (120 \pi t)\), with i in amperes and \(t\) in seconds, is placed next to a second coil, end to end. At \(\mathrm{t}=0.740 \mathrm{~s}\), a. lab tech measures the emf across the second coil, and the result is \(\mathscr{E}=-3.70 \mathrm{~V} .\) What is the mutual inductance (in \(\mathrm{mH}\) ) of the coils?

Answer 1