*31 (a) At what frequency would a 6.0 mH inductor and a 10 µF capacitor have the same reactance? (b) What would the reactance be? (c) Show that this frequency would be the nat- ural frequency of an oscillating circuit with the same L and C. .

Check Your Understanding What happens to the resonant frequency of an RLC series circuit when the following quantities are increased by a factor of 4: (a) the capacitance, (b) the self-inductance, and (c) the resistance?

Can a circuit e1eent have both capacitance and inductance?

An RLC series circuit consists of a 50 resistor, a 200F capacitor, and a 120-mN inductor whose coil has a resistance of 20. The source for the circuit has an tins emf of 240 V at a frequency of 60 Hz. Calculate the tins voltages across the (a) resistor, (b) capacitor, and (c) inductor.

In an LC circuit, what determines the frequency and the amplitude of the energy oscillations in either the inductor or capacitor?

An LC circuit in an AM tuner (in a car stereo) uses a coil with an inductance of 2.5 mH and a variable capacitor. If the natural frequency of the circuit is to be adjustable over the range 540 to 1600 kHz (the AM broadcast band), that range of capacitance is required?

Check Your Understanding The angular frequency of the oscillations in an LC circuit is 2.0103rad/s . (a) If L = 0.10H, what is C? (b) Suppose that at t = 0, all the is stored in the inductor. What is the value of ? (c) A second identical capacitor is connected in parallel with the original capacitor. What is the angular frequency of this circuit?

Explain why at high frequencies a capacitor acts as an ac short, whereas an inductor acts as an open circuit.

Calculate the rms currents for an ac source is given by v(t)=v0sint , where V0=100V and =200rad/s when connected across (a) a 20F capacitor, (b) a 20-mH inductor, and (c) a 50 resistor.

When a camera uses a flash, a fully charged capacitor discharges through an inductor. In what time must the 0.100-A current through a 2.00-mH inductor be switched on or off to induce a 500-V emf?