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Test9Solution

# Test9Solution - Solution of ECE 300 Test 9 F09 1 With...

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Solution of ECE 300 Test 9 F09 1. With reference to the circuit below, find numerical values for the following. v C 0 + ( ) = ____________ V , i L 0 + ( ) = ____________ A v L 0 + ( ) = ____________ V , i C 0 + ( ) = ____________ A d dt i L t ( ) ( ) t = 0 + = ____________ A/s , d dt v C t ( ) ( ) t = 0 + = ____________ V/s d dt i C t ( ) ( ) t = 0 + = ____________ A/s , d dt v L t ( ) ( ) t = 0 + = ____________ V/s v C + ( ) = ____________ V , i L + ( ) = ____________ A The damping factor α = ____________ /s. The natural radian frequency ω 0 = ____________ /s v 1 t ( ) = 15u t ( ) V , v 2 t ( ) = 5 V R = 20 Ω , L = 200mH , C = 10 μ F Before t = 0 all voltages and currents are constant, the capacitor is an open circuit and the inductor is a short circuit. There is no current through the capacitor and therefore no current anywhere in the circuit. By KVL around the top mesh the capacitor voltage must equal 5 V and that voltage will be the same at t = 0 + . At t = 0 + the 15 V source has just turned on, the voltage across the resistor is zero by KVL in the top mesh and its current is therefore zero. KCL on the left middle node results in zero current in the capacitor. KVL around the bottom mesh yields the inductor voltage of 15 V. The derivative of the inductor current is the inductor voltage divided by the inductance or 15V / 200mH = 75 A/s . The derivative of the capacitor voltage is the capacitor current divided by the capacitance or 0A /10 μ F = 0 V/s . By KCL at the left middle node, the derivative of the capacitor current is the sum of the derivative of the inductor current and the derivative of the current to the right in the resistor. The derivative of the voltage across the resistor is zero by KVL on the top mesh. Therefore by Ohm's law the derivative of the current in the resistor is also zero and the derivative of the capacitor current is the same as the derivative of the inductor current, 75 A/s . By KVL the derivative of the inductor voltage is the sum of the derivative of v 1 t ( ) and the derivative of the voltage across the resistor, both of which are zero.

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