27. Resistors & DC Circuits

A capacitor is discharged through a 100 Ω resistor. The discharge current decreases to 25% of its initial value in 2.5 ms. What is the value of the capacitor?

An idealized ammeter is connected to a battery as shown in Fig. E$25.28$. Find the reading of the ammeter.

Imagine that a steady current I flows in a straight cylindrical wire of radius R₀ and resistivity ρ.

(a) If the current is then changed at a rate dI/dt, show that a displacement current ID exists in the wire of magnitude ε₀ρ(dI/dt).

(b) If the current in a copper wire is changed at the rate of 1.0 A/ms, determine the magnitude of ID.

(c) Determine the magnitude of the magnetic field BD created by ID at the surface of a copper wire with R₀ = 1.00 mm. Compare (as a ratio) BD with the field created at the surface of the wire by a steady current of 1.0 A.

Household wiring has sometimes used aluminium instead of copper. Using Table 25–1, find the ratio of the resistance of a copper wire to that of an aluminum wire of the same length and diameter.

A rectangular solid made of carbon has sides of lengths 1.0 cm, 2.0 cm, and 4.0 cm, lying along the x, y, and z axes, respectively (Fig. 25–36). Determine the resistance for current that passes through the solid in the y direction, (Assume the resistivity is ρ = 3.0 x 10⁻⁵ Ω•m).

Conductor resistance causes a(n) $V_{\mathrm{drop}}$ between the voltage source and the connected load. Which term best completes the sentence?

Electrocardiographs are often connected as shown in Fig. 26–78. The lead wires to the legs are said to be capacitively coupled. A time constant of 3.0 s is typical and allows rapid changes in potential to be recorded accurately. If C = 3.0μF, what value must R have? [Hint: Consider each leg as a separate circuit.]

You've decided to protect your house by placing a 5.0-m-tall iron lightning rod next to the house. The top is sharpened to a point and the bottom is in good contact with the ground. From your research, you've learned that lightning bolts can carry up to 50 kA of current and last up to 50 μs. You don't want the potential difference between the top and bottom of the lightning rod to exceed 100 V. What minimum diameter must the rod have?

Can a 1.8-mm-diameter copper wire have the same resistance as a tungsten wire of the same length? Give numerical details.

What voltage will produce 0.25 A of current through a 5400-Ω resistor?

Household wiring has sometimes used aluminium instead of copper.Typical copper wire used for home wiring in the U.S. has a diameter of 1.63 mm. What is the resistance of 125 m of this wire?