Consider the circuit shown in the figure below. Take = 10.00 V, L = 12 mH, and R = 9 22. Shown in the figure below. R ww (a) What is the inductive time constant of the circuit? (b) Calculate the current in the circuit 100 us after the switch is closed. (c) What is the value of the final steady-state current? (d) How long does it take the current to reach 75.0% of its maximum value?

You are trying to become a member of the Physics Olympics team. Your physics professor is training you and some other students by having you compete with each other to solve problems as accurately and quickly as you can. During one session, he springs the RLC circuit shown in Figure P32.47 (page 872) on you. Figure P32.47a shows the circuit with a battery as the energy source. The battery has an emf E and internal resistance r. He tells you the following, assuming switch S has been at position a for a long time: If only switch SL is closed, and switches SC and SR are open, and then switch S is thrown to position b, the time constant of the circuit is 1 = 0.200 ms. Switch S is returned to position a for a long time. Figure P32.47 If only switch SC is closed, and switches SL and SR are open, and then switch S is thrown to position b, the time constant of the circuit is 2 = 0.050 0 ms. Switch S is returned to position a for a long time. In Figure P32.47b, an AC source with a variable frequency has been added to the same circuit, and switch S is thrown to position b. Switches SC, SL, and SR are all open. At what angular frequency should the AC source be set so that the circuit exhibits resonance? Quick! Get to work!

A person with body resistance between his hands of 10.0k accidentally grasps the terminals of a20.0-kV power supply. (Do NOT do this!) (a) Draw a circuit diagram to represent the situation, (b) If the internal resistance of the power supply is 2000 , what is thecurrent through his body? (c) What is the power dissipated in his body? (d) If the power supply is to be made safe by increasing its internal resistance, what should the internal resistance be for the maximum current in this situation to be 1.00 mA or less? (e) Will this modification compromise the effectiveness of the power supply for driving low- resistance devices? Explain your reasoning.

An uncharged series RC circuit is to be connected across a battery. For each of the following changes, determine whether the time for the capacitor to reach 90% of its final charge would increase, decrease, or remain unchanged. Indicate your answers with I, D, or U, respectively. (a) The RC time constant is doubled. (b) The battery voltage is doubled. (c) A second resistor is added in series with the original resistor.

Consider the circuit below, (a) What is the initial current through resistor R2? when the switch is closed? (b) What is die current through resistor R2 when the capacitor is fully charged, long after die switch is closed? (c) What happens if the switch is opened after it has been closed for some rime? (d) If the switch has been closed for a time period long enough for the capacitor to become fully charged, and then the switch is opened, how long before the current through resistor R1 reaches half of its initial value?

In this chapter, most examples and problems involved direct current (DC). DC circuits have the current flowing in one direction, from positive to negative. When the current was changing, it was changed linearly from I=ImaxtoI=+Imax and the voltage changed linearly from V=Vmax to V=+Vmax where Vmax=ImaxR .Suppose a voltage source is placed in series with a resistor of R = 10 that supplied a current that alternated as a sine wave, for example, I(t)=(3.00A)sin(24.00st) . (a) What would a graph of the voltage drop across the resistor V(t) versus time look like? (b) What would a plot of V(t) versus I(t) for one period look like? (Hint: If you are not sure, try plotting V(t) versus I(t) using a spreadsheet.)

Referring to Figure CQ28.6, describe what happens to the lightbulb after the switch is closed. Assume the capacitor has a large capacitance and is initially uncharged. Also assume the light illuminates when connected directly across the battery terminals.

A battery has some internal resistance. (i) Clan the potential difference across the terminals of the battery be equal to its emir (a) no (b) yes, if the battery is absorbing energy by electrical transmission (c) yes, if more than one wire is connected to each let initial (e) yes, if the current in the battery is zero (e) yes, with no special condition required. (ii) Can the terminal voltage exceed the emf? Choose your answer from the same possibilities as in part (i).

A 1,00-?O voltmeter is placed in parallel with a 75.0kresistor in a circuit, (a) Draw a circuit diagram of the connection, (b) What is the resistance of the combination? If the voltage across the combination is kept the same as it was across the 75.0-kresistor alone, what is the percent increase in current? (d) If the current through the combination is kept the same as it was through the 75.0-kresistor alone, what is the percentage decrease in voltage? (e) Are the changes found in parts (c) and (d) significant? Discuss.

An ideal emf device is connected to a set of resistors as shown in Figure P29.66. Find an expression for the current through the resistor R3 in terms of the emf and the resistances.