The output of an electrocardiogram amplifier has an impedance of 45 Ω. It is to be connected to an 8.0-Ω loudspeaker through a transformer. What should be the turns ratio of the transformer?

The frequency of the ac voltage source (peak voltage Vo) in an LRC circuit is tuned to the circuit’s resonant frequency f₀ = 1 / (2π√LC). (a) Show that the peak voltage across the capacitor is Vco = VoTo/ (2πτ), where To ( =1/fo) is the period of the resonant frequency and τ = RC is the time constant for charging the capacitor C through a resistor R. (b) Define β = To/ (2πτ) so that Vco = βVo. Then β is the “amplification” of the source voltage across the capacitor. If a particular LRC circuit contains a 2.0-nF capacitor and has a resonant frequency of 5.0 kHz, what value of R will yield β = 125?

(II) (a) Show that oscillation of charge Q on the capacitor of an LRC circuit has amplitude

$Q_0=\frac{V_0}{\sqrt{(\omega R{)}^2+{({\omega }^{2}L-\frac{1}{C})}^2}}.$

At t = 0, the current through a 60.0-mH inductor is 50.0 mA and is increasing at the rate of 78.0 mA/s. What is the initial energy stored in the inductor, and how long does it take for the energy to increase by a factor of 8.0 from the initial value?

At time t = 0, the switch in the circuit shown in Fig. 30–30 is closed. After a sufficiently long time, steady currents I₁, I₂, and I₃ flow through resistors R₁, R₂, and R₃, respectively. Determine these three currents.

An average power output of 150 W is sent into a 4-Ω loudspeaker (see Fig. 25–14). What are the rms voltage and the rms current fed to the speaker at 1.0 W when the volume is turned down?

Show that the power delivered by a three-phase ac source equals a constant P = 3Vo²/2R, by combining the four equations in Section 30–11.