Assignment:
Part 1
• A circular conducting loop with radius a and resistance R2 is concentric with a circular conducting loop with radius b » a (b much greater than a) and resistance R1. A time-dependent voltage is applied to the larger loop, having a slow sinusoidal variation in time given by V(t) = V0 sin ωt, where V0 and ω are constants with dimensions of voltage and inverse time, respectively. Assuming that the magnetic field throughout the inner loop is uniform (constant in space) and equal to the field at the center of the loop, derive expressions for the potential difference induced in the inner loop and the current i through that loop.
• The conducting loop in the shape of a quartercircle shown in the figure has a radius of 20 cm and resistance of 0.8 Ω. The magnetic field strength within the dotted circle of radius 6 cm is initially 5 T. The magnetic field strength then decreases from 5 T to 1 T in 7 s.
(a) Find the magnitude of the induced current in the loop.
(b) Find the direction of the induced current in the loop.
• A short coil with radius R = 18 cm contains N = 30 turns and surrounds a long solenoid with radius r = 3.0 cm containing n = 60 turns per centimeter. The current in the short coil is increased at a constant rate from zero to i = 1.5 A in a time of t = 16 s. Calculate the induced potential difference in the long solenoid while the current is increasing in the short coil.
• In the circuit in the figure, a battery supplies Vemf = 10 V and R1 = 4.0 Ω, R2 = 4.0 Ω, and L = 2.0 H. Calculate each of the following a long time after the switch is closed.
(a) the current flowing out of the battery.
(b) the current through R1;
(c) the current through R2;
(d) the potential difference across R1;
(e) the potential difference across R2;
(f) the potential difference across L;
(g) the rate of current change across R1.
• An emf of 30 V is applied to a coil with an inductance of 34 mH and a resistance of 0.70 Ω.
(a) Determine the energy stored in the magnetic field when the current reaches one fourth of its maximum value.
(b) How long does it take for the current to reach this value?
• A motor has a single loop inside a magnetic field of magnitude 0.95 T. If the area of the loop is 200. cm2, find the maximum angular speed possible for this motor when connected to a source of emf providing 210 V.
Part 2
• A 18-µF capacitor is fully charged by a 12-V battery and is then disconnected from the battery and allowed to discharge through a 0.9-H inductor. Find the first three times when (the magnitude of) the charge on the capacitor is 78-µC, taking t = 0 as the instant when the capacitor is connected to the inductor.
• A 2.10-µF capacitor was fully charged by being connected to a 12.0-V battery. The fully charged capacitor is then connected in series with a resistor and an inductor: R = 53 Ω and L = 0.240 H. Calculate the damped frequency of the resulting circuit.
• A capacitor with capacitance C = 6. 10-6 F is connected to an AC power source having a peak value of 13 V and f = 120 Hz. Find the reactance of the capacitor and the maximum current in the circuit.
• Design an RC high-pass filter that passes a signal with frequency 9 kHz, has a ratio Vout/Vin = 0.5, and has an impedance of 4.9 kΩ at very high frequencies.
(a) What components will you use?
(b) What is the phase of Vout relative to Vin at the frequency of 9 kHz?
• A circuit contains a 100-Ω resistor, a 0.0510-H inductor, a 0.450-µF capacitor, and a source of time-varying emf connected in series. The time-varying emf is 55.0 V at a frequency of 2000 Hz.
(a) Determine the current in the circuit.
(b) Determine the voltage drop across each component of the circuit.
(c) How much power is drawn from the source of emf?
• A transformer has 820 turns in the primary coil and 34 turns in the secondary coil.
(a) What happens if an AC voltage of 100 V is across the primary coil?
(b) If the initial AC current is 2 A, what is the output current?
(c) What happens if a DC current at 100 V flows into the primary coil?
(d) If the initial DC current is 2 A, what is the output current?