What must be the capacitance (in pFmathrm{pF}pF ) of the circuit so that the radio is tuned to a frequency of f=6.95MHzmathrm{f}=6.95 mathrm{MHz}f=6.95MHz ?

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 $\mathrm{p}\mathrm{F}$ ) of the circuit so that the radio is tuned to a frequency of $\mathrm{f}=6.95\mathrm{M}\mathrm{H}\mathrm{z}$ ?

2. A conducting coil, with current i(t)=4.20∗e0.0250tsin⁡(120πt)i(t)=4.20 * e^{0.0250 t} sin (120 pi t)i(t)=4.20∗e0.0250tsin(120πt), 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 $\mathcal{E}=-3.70\mathrm{V}.$ What is the mutual inductance (in $\mathrm{m}\mathrm{H}$ ) of the coils?

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