Measurements 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 R_V as the voltmeter’s internal resistance.]

[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 V_T = 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 V_T be if you connect a load to the 3.0-V output, assuming the load has a resistance of 7.0Ω?

[In these Problems neglect the internal resistance of a battery unless the Problem refers to it.]

(II) What is the net resistance of the circuit connected to the battery in Fig. 26–46?

(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.]

Consider two unequal resistors, of resistance R₁ and R₂, that are connected either in series or in parallel. Fill in the Table below assuming the electric potential on the low-voltage end of the combination is V_A volts and the potential at the high-voltage end of the combination is V_B volts. First draw diagrams.

The capacitor in FIGURE P28.73 begins to charge after the switch closes at t = 0 s. Find an expression for the current I at time t. Graph I from t = 0 to t = 5τ.

(II) How long does it take for the energy stored in a capacitor in a series RC circuit (Fig. 26–65) to reach 75% of its maximum value? Express answer in terms of the time constant $\tau =RC$.

<IMAGE>

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 300 μF capacitor is charged to 9.0 V, then connected in parallel with a 5000 Ω resistor. The capacitor will discharge because the resistor provides a conducting pathway between the capacitor plates, but much more slowly than if the plates were connected by a wire. Let t=0 s be the instant the fully charged capacitor is first connected to the resistor. At what time has the capacitor voltage decreased by half, to 4.5 V?