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A variable capacitor with a range from 12 to 450 pF is used with a coil to form a variable-frequency LC circuit to tune the input to a radio. (a) What is the ratio of maximum frequency to minimum frequency that can be obtained with such a capacitor? If this circuit is to obtain frequencies from 0.50 MHz to 1.36 MHz, the ratio computed in (a) is too large. By adding a capacitor in parallel to the variable capacitor, this range can be adjusted. To obtain the desired frequency range, (b) what capacitance in picofarads should be added and (c) what inductance should the coil have? Figure (a) shows the current i that is produced in a wire of resistivity 1.9 x 10-8 0.m. The magnitude of the current versus time t is shown in Figure (b). The vertical axis scale is set by is is = 5.0 A, and the horizontal axis scale is set by ts = 40 ms. Point P is at radial distance 8.0 mm from the wire's center. Determine the magnitude of the magnetic field B; at point P due to the actual current i in the wire at (a) t = 16 ms, (b) t = 32 ms, and (c) t = 48 ms. Next, assume that the electric field driving the current is confined to the wire. Then determine the magnitude of the magnetic field Bid at point P due to the displacement current id in the wire at (d) t = 16 ms, (e) t = 32 ms, and (f) t = 48 ms. At point Pat t = 16 s, what is the direction (into or out of the page) of (g) B; and (h) Bid? P. Wire (a) i (A) 0 ts t (ms) (b)In an oscillating LC circuit, L = 30.2 mH and C = 10.8 uF. At time t = O the current is 11.9 mA, the charge on the capacitor is 2.96 uC, and the capacitor is charging. What are (a) the total energy in the circuit, (b) the maximum charge on the capacitor, and (c) the maximum current? (d) If the charge on the capacitor is given by q = Q cos(wt + (p), what is the phase constant (p? (e) Suppose the data are the same, except that the capacitor is discharging at t = 0. What then is (p