27. Resistors & DC Circuits

Sketch the resistance as a function of current, for V > 0, for the diode shown in Fig. 40–38.

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?

A resistor has a current through it of 5 A. If the EMF across the resistor is 10 V, what is the resistance of this resistor?

Two resistors are made of the same material, one twice as long as the other. If the current through the shorter resistor is 5 A, what is the current through the longer resistor if they both have the same potential difference and cross-sectional area?

A copper transmission cable $100$ km long and $10.0$ cm in diameter carries a current of $125$ A. How much electrical energy is dissipated as thermal energy every hour?

What is the resistance of a carbon rod at $25.8$°C if its resistance is $0.0160\Omega$ at $0.0$°C?

A hollow aluminum cylinder is $2.50$ m long and has an inner radius of $2.75$ cm and an outer radius of $4.60$ cm. Treat each surface (inner, outer, and the two end faces) as an equipotential surface. At room temperature, what will an ohmmeter read if it is connected between (a) the opposite faces and (b) the inner and outer surfaces?

In household wiring, copper wire $2.05$ mm in diameter is often used. Find the resistance of a $24.0$-m length of this wire.

A ductile metal wire has resistance $R$. What will be the resistance of this wire in terms of $R$ if it is stretched to three times its original length, assuming that the density and resistivity of the material do not change when the wire is stretched? (Hint: The amount of metal does not change, so stretching out the wire will affect its cross-sectional area.)