15.3 RLC Series Circuits with AC

Find the voltages across the resistor, the capacitor, and the inductor in the circuit of the figure using $v \left(t\right) = V_{0} \text{sin} \omega t$ as the output of the ac generator.

In an RLC series circuit, can the voltage measured across the capacitor be greater than the voltage of the source? Answer the same question for the voltage across the inductor.

A resistor and capacitor are connected in series across an ac generator. The emf of the generator is given by $v \left(t\right) = V_{0} \text{cos} \omega t ,$ where $V_{0} = 120 \text{V},$ $\omega = 120 \pi \text{rad}/\text{s} ,$ $R = 400 \Omega$, and $C = 4.0 \mu \text{F}$. (a) What is the impedance of the circuit? (b) What is the amplitude of the current through the resistor? (c) Write an expression for the current through the resistor. (d) Write expressions representing the voltages across the resistor and across the capacitor.

In an RLC series circuit, the voltage amplitude and frequency of the source are 100 V and 500 Hz, respectively, an $R = 500 \Omega ,$ $L = 0.20 \text{H},$ and $C = 2.0 \mu \text{F} .$ (a) What is the impedance of the circuit? (b) What is the amplitude of the current from the source? (c) If the emf of the source is given by $v \left(t\right) = \left(100 \text{V}\right) \text{sin} 1000 \pi t$, how does the current vary with time? (d) Repeat the calculations with C changed to $0.20 \mu \text{F} .$