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Extra Review Problems for Electromagnetism 1. Three 425 F capacitors are connected in parallel to a 6.00 V battery. What is the equivalent capacitance? What is the charge on each capacitor? What is the voltage on each capacitor? 2. Three 425 F capacitors are connected in series to a 6.00 V battery. What is the equivalent capacitance? What is the charge on each capacitor? What is the voltage on each capacitor? 3. Three 425 F capacitors are connected in the combination shown to a 6.00 V battery. What is the equivalent capacitance? What is the charge on each capacitor? What is the voltage on each capacitor? 4. A 425 F capacitor is charged to 6.00 V. It is then discharged through a 20.0 M resistor. A) Find the time constant. B) Find the initial charge on the plates. C) Find the charge on the plates exactly one time constant after discharge has begun. D) What percent of the original charge is this? E) Find the capacitor’s voltage 4250 s after discharge begins. F) Find the instantaneous current at t = 4250 s. G) Find the half-life of the capacitor’s voltage. 5. Sketch a bar magnet with its magnetic field lines. Be sure to label the poles correctly. 6. Sketch the magnetic field lines in the solenoid shown here. Assume the current enters on the left and exits on the right. Explain how the right hand rule works. 7. A +32 C charge having a velocity of 2.5104 m s-1 enters an external magnetic field having a magnetic flux density of 0.75 T. Find the magnitude of the magnetic force acting on the charge as it is in the field. Sketch in the direction that the charge will follow as it passes through the field. Explain how the right hand rule works. What will its speed be when it exits the field? 8. The diagram shows three parallel wires P, Q, and R, each having the same current I. What is the direction of the resultant force on wire Q due to wire P and wire R? 9. A wire having a length of 20.0 m is propelled through the air in a direction perpendicular to its length at 150. m/s in a magnetic field that is perpendicular to the plane of its velocity, and having a strength of 0.015 T. A) What is the induced emf in the wire? B) If a resistor of 12.0 is connected to the ends of the wire, what will its current be? C) What would be the power dissipated in the resistor? 10. A coil of wire resting on a tabletop and having 100 turns and an area of 3.14 cm 2 is immersed in a magnetic field (0.90 T) which is pointing upward. A) What is the angle that the magnetic field makes with the direction of the area? B) What is the flux through a single loop? C) What is the flux linkage through the coil? D) What is the induced emf if the magnetic field remains constant? E) If the magnetic field decreases to 0.45 T in 0.25 s, what is the rate of change of the flux linkage through the coil? F) What, then, is the induced emf? G) What is the direction of the induced current in the coil, as viewed from above the table? H) Which law tells you this? 11. A coil having 250 turns is subjected to a time-dependent magnetic flux as shown in the graph. A) What is the flux at t = 0.0015 s? B) What is the flux linkage at t = 0.0015 s? C) What is the magnitude of the emf induced in the coil? I/A em f / V 12. The graphs of voltage and current for an ac circuit containing a resistor are shown. A) Find the rms voltage corresponding to the 40 induced emf whose graph is shown. B) Find the peak voltage. 20 C) Find the angular frequency of the coil that 20 0 is producing this emf. 30 10 D) Find the maximum flux linkage of the coil -20 that is producing this emf. E) Find the rms current from the graph. -40 F) Find the peak current. 2 G) Write the equation which shows the time variation of the current. 1 H) Find the resistance of the circuit. 20 0 I) What is the average power dissipated by the 30 10 circuit? 40 t / ms 40 t / ms -1 -2 13. A transformer having 250 turns in its primary winding has a 60 Hz input voltage of Vin = 120 VAC. It is desired that Vout should be 16 VAC. A) How many turns should the secondary winding have? B) If the current in the primary winding is 1.25 A, what will the current in the secondary winding be? C) What is the frequency of the output voltage? D) If the frequency doubles, describe how this will affect power losses. Vin Primary Vout Secondary