30. Induction and Inductance

An L-R-C series circuit has L = 0.450 H, C = 2.50 × 10^-5 F, and resistance R. What value must R have to give a 5.0% decrease in angular frequency compared to the value calculated in part (a)?

An L-R-C series circuit has L = 0.450 H, C = 2.50 × 10^-5 F, and resistance R. What is the angular frequency of the circuit when R = 0?

An L-R-C series circuit has L = 0.600 H and C = 3.00 mF. What value of R gives critical damping?

An L-R-C series circuit has L = 0.600 H and C = 3.00 mF. Calculate the angular frequency of oscillation for the circuit when R = 0.

FIGURE CP32.68 shows voltage and current graphs for a series RLC circuit. What is the resistance R?

Show that the peak inductor voltage in a series RLC circuit is maximum at frequency ${\omega }_L={(\frac{1}{{\omega }_0^2}-\frac{1}{2}{R}^2{C}^2)}^{-1/2}$.

Prove that the energy dissipation is a maximum at ω = ω₀.

A series RLC circuit with ε₀ = 10.0 V consists of a 1.0 Ω resistor, a 1.0 μH inductor, and a 1.0 μF capacitor. What is V₁ at ω = ω₀ and at ω = ω₁?

The switch in FIGURE EX30.32 has been in position 1 for a long time. It is changed to position 2 at t = 0 s. What is the first time at which the current is maximum?

For the circuit shown in Fig. 30–35, show that if the condition R₁ R₂ = L/C is satisfied then the potential difference between points a and b is zero for all frequencies.