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.

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?

An ac voltage source V = Vo sin (ωt + 90°) is connected across an inductor L and current I = Io sin (ωt) flows in this circuit. Note that the current and source voltage are 90° out of phase.

(a) Directly calculate the average power delivered by the source over one period T of its sinusoidal cycle via the integral P = ∫₀ᵀ VI dt/T.

(b) Apply the relation P = Iᵣₘₛ Vᵣₘₛ cos Φ to this circuit and show that the answer you obtain is consistent with that found in part (a). Comment on your results.

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?

A pair of straight parallel thin wires, such as a lamp cord, each of radius r, are a distance 𝓁 apart and carry current to a circuit some distance away. Ignoring the field within each wire, show that the inductance per unit length is (μ₀/π) ln[(𝓁 - r) /r].

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.

For an underdamped LRC circuit, determine a formula for the energy U = UE + UB stored in the electric and magnetic fields as a function of time. Give answer in terms of the initial charge Q_o on the capacitor.