A charged capacitor is connected to a resistor and a switch as in the figure below. The circuit has a time constant of 2.50 s. Soon after the switch is closed, the charge on the capacitor is 81.0% of its initial charge +Q (a) Find the time interval required for the capacitor to reach this charge. (b) If R= 200 kn, what is the value of C? C =

A charged capacitor is connected to a resistor and a switch as in the figure below. The circuit has a time constant of 2.50 s. Soon after the switch is closed, the charge on the capacitor is 81.0% of its initial charge +Q (a) Find the time interval required for the capacitor to reach this charge. (b) If R= 200 kn, what is the value of C? C =

Physics for Scientists and Engineers

10th Edition

ISBN:9781337553278

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter27: Direct-current Circuits

Section: Chapter Questions

Problem 44AP: A battery is used to charge a capacitor through a resistor as shown in Figure P27.44. Show that half...

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Consider the circuit shown in Figure P26.24, where C1, = 6.00 F, C2 = 3.00 F. and V = 20.0 V. Capacitor C1 is first charged by closing switch S1. Switch S1 is then opened, and the charged capacitor is connected to the uncharged capacitor by closing Calculate (a) the initial charge acquired by C, and (b) the final charge on each capacitor.
A battery is used to charge a capacitor through a resistor as shown in Figure P27.44. Show that half the energy supplied by the battery appears as internal energy in the resistor and half is stored in the capacitor. Figure P27.44
A charge Q is placed on a capacitor of capacitance C. The capacitor is connected into the circuit shown in Figure P26.37, with an open switch, a resistor, and an initially uncharged capacitor of capacitance 3C. The switch is then closed, and the circuit comes to equilibrium. In terms of Q and C, find (a) the final potential difference between the plates of each capacitor, (b) the charge on each capacitor, and (c) the final energy stored in each capacitor. (d) Find the internal energy appearing in the resistor. Figure P26.37
Consider the circuit shown in Figure P20.52, where C1 = 6.00 F, C2 = 3.00 F, and V = 20.0 V. Capacitor C1 is first charged by closing switch S1. Switch S1 is then opened, and the charged capacitor is connected to the uncharged capacitor by closing S2. Calculate (a) the initial charge acquired by C1 and (b) the final charge on each capacitor. Figure P20.52
A Pairs of parallel wires or coaxial cables are two conductors separated by an insulator, so they have a capacitance. For a given cable, the capacitance is independent of the length if the cable is very long. A typical circuit model of a cable is shown in Figure P27.87. It is called a lumped-parameter model and represents how a unit length of the cable behaves. Find the equivalent capacitance of a. one unit length (Fig. P27.87A), b. two unit lengths (Fig. P27.87B), and c. an infinite number of unit lengths (Fig. P27.87C). Hint: For the infinite number of units, adding one more unit at the beginning does not change the equivalent capacitance.
(a) Determine the equilibrium charge on the capacitor in the circuit of Figure P27.46 as a function of R. (b) Evaluate the charge when R = 10.0 . (c) Can the charge on the capacitor be zero? If so, for what value of R? (d) What is the maximum possible magnitude of the charge on the capacitor? For what value of R is it achieved? (c) Is it experimentally meaningful to take R = ? Explain your answer. If so, what charge magnitude does it imply? Figure P27.46
Draw two graphs of charge versus time on a capacitor. Draw one for charging an initially uncharged capacitor in series with a resistor, as in the circuit in Figure 21.38, starting from t = 0. Draw the other for discharging a capacitor through a resistor, as in the circuit in Figure 21.39, starting at t = 0, with an initial charge Q0. Show at least two intervals of t.
The circuit in Figure P27.35 has been connected for several seconds. Find the current (a) in the 4.00-V battery, (b) in the 3.00- resistor, (c) in the 8.00-V battery, and (d) in the 3.00-V battery. (e) Find the charge on the capacitor. Figure P27.35
The- pair of capacitors in Figure P28.63 are fully charged by a 12.0-V battery. The battery is disconnected, and the switch is then closed. Alter 1.00 ms has elapsed, (a) how much charge remains 011 the 3.00-F capacitor? (b) How much charge remains on the 2.00-F capacitor? (c) What is the current in the resistor at this time?
The circuit in Figure P27.85 shows four capacitors connected to a battery. The switch S is initially open, and all capacitors have reached their final charge. The capacitances are C1 = 6.00 F, C2 = 12.00 F, C3 = 8.00 F, and C4 = 4.00 F. a. Find the potential difference across each capacitor and the charge stored in each. b. The switch is now closed. What is the new final potential difference across each capacitor and the new charge stored in each? Figure P27.85
A capacitor with initial charge Q0 is connected across a resistor R at time t = 0. The separation between the plates of the capacitor changes as d = d0/(1 + t) for 0 t 1 s. Find an expression for the voltage drop across the capacitor as a function of time.
A circuit contains a D-cell battery, a switch, a 20- resistor, and three 20-mF capacitors. The capacitors are connected in parallel, and the parallel connection of capacitors are connected in series with the switch, the resistor and the battery, (a) What is die equivalent capacitance of the circuit? (b) What is the KC time constant? (c) How long before the current decreases to 50% of the initial value once the switch is closed?