BackMeasurements made on circuits that contain large resistances can be confusing. Consider a circuit powered by a battery ε = 15.000 V with a 10.00-MΩ resistor in series with an unknown resistor R. As shown in Fig. 26–92, a particular voltmeter reads V1 = 366 mV when connected across the 10.00 -MΩ resistor and this meter reads V2 = 7.317 V when connected across R. Determine the value of R. [Hint: Define RV as the voltmeter’s internal resistance.]
(III) Determine the net resistance in Fig. 26–61 (a) between points a and c, and (b) between points a and b. Assume R' ≠ R. [Hint: Apply an emf between the two points in each case and determine currents; use symmetry at junctions.]
A galvanometer has a sensitivity of 45kΩ/V and internal resistance 20.0 Ω. How could you make this into an ammeter that reads 1.0 A full scale?
[In these Problems neglect the internal resistance of a battery unless the Problem refers to it.]
(II) A power supply has a fixed output voltage of 12.0 V, but you need VT = 3.0 V output for an experiment. (a) Using the voltage divider shown in Fig. 26–47, what should R₂ be if R₁ is 16.5 Ω? (b) What will the terminal voltage VT be if you connect a load to the 3.0-V output, assuming the load has a resistance of 7.0Ω?
A copper pipe has an inside diameter of 3.00 cm and an outside diameter of 5.00 cm (Fig. 25–39). What is the resistance to a dc current of a 12.0-m length of this pipe?.
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?
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?
Small changes in the length of an object can be measured using a strain gauge sensor, which is a wire that when undeformed has length ℓ₀, cross-sectional area A₀, and resistance R₀. This sensor is rigidly affixed to the object’s surface, aligning its length in the direction in which length changes are to be measured. As the object deforms, the length of the wire sensor changes by Δℓ, and the resulting change ΔR in the sensor’s resistance is measured. Assuming that as the solid wire is deformed to a length ℓ, its density and volume remain constant (only approximately valid), show that the strain ( = Δℓ / ℓ₀ ) of the wire sensor, and thus of the object to which it is attached, is approximately ΔR / 2R₀.
What is the time constant for the discharge of the capacitors in FIGURE EX28.34?
A 12.0-V battery (assume the internal resistance = 0) is connected to two resistors in series. A voltmeter whose internal resistance is 18.0 kΩ measures 5.5 V and 4.0 V, respectively, when connected across each of the resistors in turn. What is the resistance of each resistor?
(II) Suppose two batteries, with unequal emfs of 2.00 V and 3.00 V, are connected as shown in Fig. 26–63. If each internal resistance is r = 0.350Ω and R = 4.00Ω, what is the voltage across the resistor R?
Two of the three resistors in FIGURE EX28.23 are unknown but equal. The total resistance between points 1 and 2 is 75Ω. What is the value of R?
What is the voltage of the battery below?
The level of liquid helium (temperature ≈ 4K) in its storage tank can be monitored using a vertically aligned niobium–titanium (NbTi) wire, whose length ℓ spans the height of the tank. In this level-sensing setup, an electronic circuit maintains a constant electrical current I at all times in the NbTi wire and a voltmeter monitors the voltage V across this wire. The NbTi wire is superconducting ( R = 0) if below its transition temperature of 10 K, so the portion of the wire immersed in the liquid helium is in the superconducting state, while the portion above the liquid (in helium vapor with temperature above 10 K) is in the normal state. Define ƒ = x/ℓ to be the fraction of the tank filled with liquid helium (Fig. 25–40) and V₀ to be the value of the voltage V when the tank is empty (ƒ = 0) . Determine the relation between f and V (in terms of V₀).
The capacitor in an RC circuit is discharged with a time constant of 10 ms. At what time after the discharge begins are (a) the charge on the capacitor reduced to half its initial value and (b) the energy stored in the capacitor reduced to half its initial value?