A parallel-plate capacitor is filled with a dielectric of dielectric constant K and high resistivity ρ (it conducts very slightly). This capacitor can be modeled as a pure capacitance C in parallel with a resistance R. Assume a battery places a charge +Q and -Q on the capacitor’s opposing plates and is then disconnected. Show that the capacitor discharges with a time constant = K∊₀ρ (known as the dielectric relaxation time). Evaluate if the dielectric is glass with ρ = 1.0 x 1012 Ωm and K = 5.0.
27. Resistors & DC Circuits
Solving Resistor Circuits
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Cardiac defibrillators are discussed in Section 24–4. Choose a value for the resistance so that the 1.4-μF capacitor can be charged to 3100 V in 2.0 seconds. Assume that this 3100 V is 95% of the full source voltage.
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A 10.0-m length of wire consists of 5.0 m of copper followed by 5.0 m of aluminum, both of diameter 1.4 mm. A voltage difference of 75 mV is placed across the composite wire. (a) What is the total resistance (sum) of the two wires? (b) What is the current through the wire? (c) What are the voltages across the aluminum part and across the copper part?
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A 2.5-kΩ and a 3.7-kΩ resistor are connected in parallel; this combination is connected in series with a 1.4-kΩ resistor. If each resistor is rated at 1.0 W (maximum without overheating), what is the maximum voltage that can be applied across the whole network?
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Three 2.20-kΩ resistors can be connected together in four different ways, making combinations of series and/or parallel circuits. What are these four ways, and what is the net resistance in each case?
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Neglect the internal resistance of a battery unless the Problem refers to it. Two resistors when connected in series to a 120-V line use one-fourth the power that is used when they are connected in parallel. If one resistor is 4.3 kΩ, what is the resistance of the other?
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Three 45-Ω lightbulbs and three 65-Ω lightbulbs are connected in series. What is the total resistance if all six are wired in parallel?
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Three 45-Ω lightbulbs and three 65-Ω lightbulbs are connected in series. What is the total resistance of the circuit?
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To which two points in the circuit of FIGURE P28.45 should a 12 V battery be connected to dissipate the most power?
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A typical small flashlight contains two batteries, each having an emf of 1.5 V, connected in series with a bulb having resistance 17 Ω. The resistance of real batteries increases as they run down. If the initial internal resistance is negligible, what is the combined internal resistance of both batteries when the power to the bulb has decreased to half its initial value?
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(III) If the 25-Ω resistor in Fig. 26–59 is shorted out (resistance = 0 ), what then would be the current through the 15-Ω resistor?
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Cardiac defibrillators are discussed in Section 24–4. The effective resistance of the human body is given in Section 26–6. If the defibrillator discharges with a time constant of 12 ms, what is the effective capacitance of the human body?
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A typical voltmeter has an internal resistance of 10 MΩ and can only measure potential differences of up to several hundred volts. Figure 26–93 shows the design of a probe to measure a very high voltage V using a voltmeter. If you want the voltmeter to read 50 V when V = 50 kV , what value R should be used in this probe?
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The current through the 4.0-kΩ resistor in Fig. 26–74 is 2.85 mA. What is the terminal voltage Vba of the “unknown” battery? (There are two answers. Why?)
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Suppose the switch S in Fig. 26–70 is closed. What is the time constant (or time constants) for charging the capacitors after the 24 V is applied?
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