110203_hw3 - a At t=t the switch is flipped to position 1...

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February 3, 2011 PHYS 4132 Homework 3 Due date: February 10, 2011 1. In class we discussed a serial resonant circuit consisting of a resistance, an inductance and a capacitance. At time t 0 the capacitor is fully charged (U 0 ). (i) In case of weak damping and following the discussion in class derive an expression for a. U C the potential difference across the capacitor plates as function of time b. the phase φ, c. the current I flowing through the circuit. Show all intermediate steps in detail. (ii) F or the case of strong damping (β 2 > ω 0 2 ) derive an expression for the potential difference across the capacitor plates as function of time. 2. A circuit consists of a DC voltage source U 0 , an ohmic resistance R and a capacitance C in series as shown in the diagram.
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Unformatted text preview: a. At t=t the switch is flipped to position 1. Calculate the potential difference U C across the capacitor plates and U R across the ohmic resistor as well as the current I as function of time. b. At t=t 1 ( U C (t1) = U ) the switch is flipped into position 2. Calculate U C , U R and I as function of time. 3. A serial circuit consists of a capacitor, a resistor and a switch. a. The capacitor is made from two flat square metal plates of length L on a side and separated by a distance d . What is the capacitance ? b. Show that if any electrical energy is stored in the capacitor, it is entirely dissipated in the resistor after the switch is closed....
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