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In the figure, the battery has an emf of 14.0 V, the inductance is 2.65 mH, and the capacitance is 8.10 pF. The switch has been set to position a for a long time so that the capacitor is charged. The switch is then thrown to position b, removing the battery from the circuit and connecting the capacitor directly across the inductor. First the capacitor is fully charged with the switch set to position a. Then, the switch is thrown position b and the battery is no longer in the circuit. (a) Find the frequency of oscillation of the circuit. SOLUTION Conceptualize When the switch is thrown to position b, the active part of the circuit is the right-hand loop, which is what kind of circuit? O RLC O LC O RL Categorize We use equations developed in this section, so we categorize this example as -Select- v problem. Analyze (Use the following as necessary: L and C. Do not substitute numerical values; use variables only.) to find the frequency (in Hz): V LC Use = Substitute numerical values (Enter your answer in MHz.): MHz (b) What are the maximum values of charge on the capacitor and current in the circuit? SOLUTION Find the initial charge (in pC) on the capacitor, which equals the maximum charge: Omax = CAV = pC Use -wQmax sin(@t) = -Imay Ssin(@t) to find the maximum current (in pA) from the maximum charge: Imax = oQmax = 2xf Qmay = HA

In the figure, the battery has an emf of 14.0 V, the inductance is 2.65 mH, and the capacitance is 8.10 pF. The switch has been set to position a for a long time so that the capacitor is charged. The switch is then thrown to position b, removing the battery from the circuit and connecting the capacitor directly across the inductor. First the capacitor is fully charged with the switch set to position a. Then, the switch is thrown position b and the battery is no longer in the circuit. (a) Find the frequency of oscillation of the circuit. SOLUTION Conceptualize When the switch is thrown to position b, the active part of the circuit is the right-hand loop, which is what kind of circuit? O RLC O LC O RL Categorize We use equations developed in this section, so we categorize this example as -Select- v problem. Analyze (Use the following as necessary: L and C. Do not substitute numerical values; use variables only.) to find the frequency (in Hz): V LC Use = Substitute numerical values (Enter your answer in MHz.): MHz (b) What are the maximum values of charge on the capacitor and current in the circuit? SOLUTION Find the initial charge (in pC) on the capacitor, which equals the maximum charge: Omax = CAV = pC Use -wQmax sin(@t) = -Imay Ssin(@t) to find the maximum current (in pA) from the maximum charge: Imax = oQmax = 2xf Qmay = HA

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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In the figure, the battery has an emf of 14.0 V, the inductance is 2.65 mH, and the capacitance is 8.10 pF. The switch has been set to position a for a long time so that the capacitor is charged. The switch is then thrown to position b, removing the battery from the circuit and connecting the capacitor directly across the inductor. First the capacitor is fully charged with the switch set to position a. Then, the switch is thrown to position b and the battery is no longer in the circuit. a + (a) Find the frequency of oscillation of the circuit. SOLUTION Conceptualize When the switch is thrown to position b, the active part of the circuit is the right-hand loop, which is what kind of circuit? RLC LC RL Categorize We use equations developed in this section, so we categorize this example as ---Select--- v problem. Analyze (Use the following as necessary: L and C. Do not substitute numerical values; use variables only.) 1 to find the frequency (in Hz): V LC Use w = 1 f = Substitute numerical values (Enter your answer in MHz.): f = MHz (b) What are the maximum values of charge on the capacitor and current in the circuit? SOLUTION Find the initial charge (in pC) on the capacitor, which equals the maximum charge: Qmax C AV = pC Use -@Qmax sin(@t) = -I sin(@t) to find the maximum current (in µA) from the maximum charge: max Imax = 0emax 2nf Qmax HA %D max ll
Transcribed Image Text:In the figure, the battery has an emf of 14.0 V, the inductance is 2.65 mH, and the capacitance is 8.10 pF. The switch has been set to position a for a long time so that the capacitor is charged. The switch is then thrown to position b, removing the battery from the circuit and connecting the capacitor directly across the inductor. First the capacitor is fully charged with the switch set to position a. Then, the switch is thrown to position b and the battery is no longer in the circuit. a + (a) Find the frequency of oscillation of the circuit. SOLUTION Conceptualize When the switch is thrown to position b, the active part of the circuit is the right-hand loop, which is what kind of circuit? RLC LC RL Categorize We use equations developed in this section, so we categorize this example as ---Select--- v problem. Analyze (Use the following as necessary: L and C. Do not substitute numerical values; use variables only.) 1 to find the frequency (in Hz): V LC Use w = 1 f = Substitute numerical values (Enter your answer in MHz.): f = MHz (b) What are the maximum values of charge on the capacitor and current in the circuit? SOLUTION Find the initial charge (in pC) on the capacitor, which equals the maximum charge: Qmax C AV = pC Use -@Qmax sin(@t) = -I sin(@t) to find the maximum current (in µA) from the maximum charge: max Imax = 0emax 2nf Qmax HA %D max ll
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