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### 5 Cards in this Set

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 The energy in an oscillating LC circuit containing a 1.25 H inductor is 5.70 uJ. The maximum charge on the capacitor is 175 uC. For a mechanical system with the same period, find the (a) mass, (b) spring constant, (c) maximum displacement, and (d) maximum speed. 31.7 (a) 1.25 kg; (b) 372 N/m; (c) 1.75 × 10 –4 m; (d) 3.02 mm/s An oscillating LC circuit consisting of a 1.0 nF capacitor and a 3.0 mH coil has a maximum voltage of 3.0 V. What are (a) the maximum charge on the capacitor, (b) the maximum current through the circuit, and (c) the maximum energy stored in the magnetic field of the coil? 31.11 (a) 3.0 nC; (b) 1.7 mA; (c) 4.5 nJ A variable capacitor with a range from 10 to 365 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 0.54 MHz to 1.60 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 should be added and (c) what inductance should the coil have? 31.15 (a) 6.0; (b) 36 pF; (c) 0.22 mH In an oscillating series RLC circuit, find the time required for the maximum energy present in the capacitor during an oscillation to fall to half its initial value. Assume q = Q at t = 0. 31.26 In an oscillating series RLC circuit, show that DU/U, the fraction of the energy lost per cycle of oscillation, is given to a close approximation by 2pR/wL. The quantity wL/R is often called the Q of the circuit (for quality). A high-Q circuit has low resistance and a low fractional energy loss (= 2p/Q) per cycle. 31.27