# Electromagnetism problems

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1) A piece of copper wire is formed into a single circular loop of radius 17 cm. A magnetic field is oriented parallel to the normal to the loop, and it increases from 0 to 0.64 T in a time of 0.65 s. The wire has a resistance per unit length of 4.9 x 10-2 OHM/m. What is the average electrical energy dissipated in the resistance of the wire?

2) A generator uses a coil that has 440 turns and a 0.48-T magnetic field. The frequency of this generator is 60.0 Hz, and its emf has an rms value of 120 V. Assuming that each turn of the coil is a square (an approximation), determine the length of the wire from which the coil is made.

3) A capacitor is connected across an ac generator whose frequency is 900 Hz and whose peak output voltage is 210 V. The rms current in the circuit is 3.0 A. (a) What is the capacitance of the capacitor? (b) What is the magnitude of the maximum charge on one plate of the capacitor? Note: The ac current and voltage are rms values and power is an average value unless indicated otherwise.

4) A 56.0-mH inductor has a reactance of 1.90 k . (a) What is the frequency of the ac current that passes through the inductor? (b) What is the capacitance of a capacitor that has the same reactance at this frequency? The frequency is tripled, so that the reactances of the inductor and capacitor are no longer equal. What are the new reactances of (c) the inductor and (d) the capacitor?

5) Two inductors are connected in parallel across the terminals of a generator. One has an inductance of L1 = 0.027 H, while the other has an inductance of L2 = 0.056 H. A single inductor, with an inductance L, is connected across the terminals of a second generator that has the same frequency and voltage as the first one. The current delivered by the second generator is equal to the total current delivered by the first generator. Find L. Note: The ac current and voltage are rms values and power is an average value unless indicated otherwise.

6) A series RCL circuit contains only a capacitor (C = 9.46 F), an inductor (L = 5.71 mH), and a generator (peak voltage = 79.2 V, frequency = 5.36 x 103 Hz). When t = 0 s, the instantaneous value of the voltage is zero, and it rises to a maximum one-quarter of a period later. (a) Find the instantaneous value of the voltage across the capacitor/inductor combination when t = 8.59 x 10-4 s. (b) What is the instantaneous value of the current when t = 8.59 x 10-4 s? (Hint: The instantaneous values of the voltage and current are the vertical components of the voltage and current phasors, respectively.) Note: The ac current and voltage are rms values and power is an average value unless indicated otherwise.

7) A series circuit contains only a resistor and an inductor. The voltage V of the generator is fixed. If R = 14 and L = 5.7 mH, find the frequency at which the current is one-half it value at zero frequency. Note: The ac current and voltage are rms values and power is an average value unless indicated otherwise.

8) The resonant frequency of a series RCL circuit is 206 Hz. When the circuit is connected to a voltage generator with a different frequency, the ratio of the inductive reactance to the capacitive reactance is observed to be 7.19. What is the frequency of the generator? Note: The ac current and voltage are rms values and power is an average value unless indicated otherwise.

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