Four identical capacitors are connected with a resistor in two different ways. When they are connected as in part a of the drawing, the time constant to charge up this circuit is 0.75 s. What is the time constant when they are connected with the same resistor as in part b? C c F (a) (b) Number i 12.0 Units

Four identical capacitors are connected with a resistor in two different ways. When they are connected as in part a of the drawing, the time constant to charge up this circuit is 0.75 s. What is the time constant when they are connected with the same resistor as in part b? C c F (a) (b) Number i 12.0 Units

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 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
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 P21.59 has been connected for a long time. (a) What is the potential difference across the capacitor? (b) If the battery is disconnected from the circuit, over what time interval does the capacitor discharge to one-tenth its initial voltage?
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
Three 100- resistors are connected as shown in Figure P21.41 The maximum power that can safely be delivered to any one resistor is 25.0 W. (a) What is the maximum potential difference that can be applied to the terminals a and b? (b) For the voltage determined in part (a), what is the power delivered to each resistor? (c) What is the total power delivered to the combination of resistors?
(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
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 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 pair of capacitors with capacitances CA = 3.70 F and CB = 6.40 F are connected in a network. What is the equivalent capacitance of the pair of capacitors if they are connected a. in parallel and b. in series?
The duration of a photographic flash is related to an RC time constant, which is 0.100F for a certain camera, (a) If the resistance of the flash lamp is 0.0400 duringdischarge, what is the size of the capacitor supplying its energy? (b) What is the time constant for charging the capacitor, if the charging resistance is 800 k ?
An oceanographer is studying how the ion concentration in seawater depends on depth. She makes a measurement by lowering into the water a pair of concentric metallic cylinders (Fig. P21.66) at the end of a cable and taking data to determine the resistance between these electrodes as a function of depth. The water between the two cylinders forms a cylindrical shell of inner radius ra, outer radius rb, and length L much larger than rb. The scientist applies a potential difference V between the inner and outer surfaces, producing an outward radial current I. Let represent the resistivity of the water. (a) Find the resistance of the water between the cylinders in terms of L, , ra, an rb. (b) Express the resistivity of the water in terms of the measured quantities L, ra, rb, V, and I. Figure P21.66