An circuit consists of a resistor (resistance R), inductor (inductance L), and capacitor (capacitance C) connected...

  

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An circuit consists of a resistor (resistance R), inductor (inductance L), and capacitor (capacitance C) connected in series with an AC source supplying sinusoidal voltage Vo cos(wt). Assume that all circuit elements are ideal, so that the [Pri only resistance in the circuit is due to the resistor. Also assume that w is the resonant frequency of the circuit. Part A What is the average power Pavg supplied by the voltage source? Part A.1 Find the instantaneous power What is the instantaneous power P (t) dissipated in the circuit? Note: You will need to use the fact that the circuit is being driven at its resonant frequency to eliminate w from your answer. Hint A.1.a A useful formula for power The power dissipated in the circuit is equal to the voltage supplied by the AC source times the current in the circuit: P = VI. Hint A.1.b The current in a driven L-R-C circuit The L-R-C circuit described in the problem introduction obeys the differential equation Io = Vo " √(WL)² + R² and tanp= ANSWER: d²q dq L + R + dt² dt where q is the charge on one of the capacitor plates. After solving this equation for q as a function of time, you can take the derivative to find the current in the circuit: I = The result is IIo cos(wt +), where = 1 WL RwC R 용 = Vo cos(wt), = Part A.1.c Determine the resonant frequency The problem introduction states that the circuit is being driven at its resonant frequency w. What is the value of w in terms of other given quantities? Express your answer in terms of any or all of the following quantities: C, L, R. w = Answer not displayed dq dt Express your answer in terms of any or all of the following quantities: Vo, C, L, R, t. P (t) = Answer not displayed ANSWER: Hint A.2 Average value of a periodic function Express your answer in terms of any or all of the following quantities: Vo, C, L, and R. Hint not displayed An circuit consists of a resistor (resistance R), inductor (inductance L), and capacitor (capacitance C) connected in series with an AC source supplying sinusoidal voltage Vo cos(wt). Assume that all circuit elements are ideal, so that the [Pri only resistance in the circuit is due to the resistor. Also assume that w is the resonant frequency of the circuit. Part A What is the average power Pavg supplied by the voltage source? Part A.1 Find the instantaneous power What is the instantaneous power P (t) dissipated in the circuit? Note: You will need to use the fact that the circuit is being driven at its resonant frequency to eliminate w from your answer. Hint A.1.a A useful formula for power The power dissipated in the circuit is equal to the voltage supplied by the AC source times the current in the circuit: P = VI. Hint A.1.b The current in a driven L-R-C circuit The L-R-C circuit described in the problem introduction obeys the differential equation Io = Vo " √(WL)² + R² and tanp= ANSWER: d²q dq L + R + dt² dt where q is the charge on one of the capacitor plates. After solving this equation for q as a function of time, you can take the derivative to find the current in the circuit: I = The result is IIo cos(wt +), where = 1 WL RwC R 용 = Vo cos(wt), = Part A.1.c Determine the resonant frequency The problem introduction states that the circuit is being driven at its resonant frequency w. What is the value of w in terms of other given quantities? Express your answer in terms of any or all of the following quantities: C, L, R. w = Answer not displayed dq dt Express your answer in terms of any or all of the following quantities: Vo, C, L, R, t. P (t) = Answer not displayed ANSWER: Hint A.2 Average value of a periodic function Express your answer in terms of any or all of the following quantities: Vo, C, L, and R. Hint not displayed

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Solution of part A To calculate the average power supplied to a voltage source for a circuit containing a resistor R inductor L and capacitor C we need to use the concepts of AC circuit analysis We kn... View the full answer