Problem 1
You have a special light bulb with a \(very\) delicate wire filament. The wire will break if the current in it ever exceeds 1.50 A, even for an instant. What is the largest root-mean-square current you can run through this bulb?
Problem 2
A sinusoidal current \(i = I\space cos\space \omega\)t has an rms value \(I_{rms} =\)2.10 A. (a) What is the current amplitude? (b) The current is passed through a full-wave rectifier circuit. What is the rectified average current? (c) Which is larger: \(I_{rms}\) or \(I_{rav}\)? Explain, using graphs of \(i^2\) and of the rectified current.
Problem 5
An inductor with \(L\) = 9.50 mH is connected across an ac source that has voltage amplitude 45.0 V. (a) What is the phase angle \(\phi\) for the source voltage relative to the current? Does the source voltage lag or lead the current? (b) What value for the frequency of the source results in a current amplitude of 3.90 A?
Problem 6
A capacitance \(C\) and an inductance \(L\) are operated at the same angular frequency. (a) At what angular frequency will they have the same reactance? (b) If \(L\) = 5.00 mH and \(C\) = 3.50 \(\mu\)F, what is the numerical value of the angular frequency in part (a), and what is the reactance of each element?
Problem 7
The wiring for a refrigerator contains a starter capacitor. A voltage of amplitude 170 V and frequency 60.0 Hz applied across the capacitor is to produce a current amplitude of 0.850 A through the capacitor. What capacitance \(C\) is required?
Problem 8
(a) Compute the reactance of a 0.450-H inductor at frequencies of 60.0 Hz and 600 Hz. (b) Compute the reactance of a 2.50-\(\mu\)F capacitor at the same frequencies. (c) At what frequency is the reactance of a 0.450-H inductor equal to that of a 2.50-\(\mu\)F capacitor?
Problem 9
(a) What is the reactance of a 3.00-H inductor at a frequency of 80.0 Hz? (b) What is the inductance of an inductor whose reactance is 120\(\Omega\) at 80.0 Hz? (c) What is the reactance of a 4.00-\(\mu\)F capacitor at a frequency of 80.0 Hz? (d) What is the capacitance of a capacitor whose reactance is 120 \(\Omega\) at 80.0 Hz?
Problem 10
You want the current amplitude through a 0.450-mH inductor (part of the circuitry for a radio receiver) to be 1.80 mA when a sinusoidal voltage with amplitude 12.0 V is applied across the inductor. What frequency is required?
Problem 11
A 0.180-H inductor is connected in series with a 90.0-\(\Omega\) resistor and an ac source. The voltage across the inductor is \(v_L\) = -(12.0 V)sin[1480 rad/s)t]. (a) Derive an expression for the voltage \(v_R\) across the resistor. (b) What is \(v_R\) at t = 2.00 ms?
Problem 12
A 250-\(\Omega\) resistor is connected in series with a 4.80-\(\mu\)F capacitor and an ac source. The voltage across the capacitor is v\(_C\) = (7.60 V)sin[120 rad/s)t]. (a) Determine the capacitive reactance of the capacitor. (b) Derive an expression for the voltage v\(_R\) across the resistor.
