A Wheatstone bridge is a type of “bridge circuit” used to make measurements of resistance. The unknown resistance to be measured, R_x, is placed in the circuit with accurately known resistances R₁, R₂ and R₃ (Fig. 26–73). One of these, R₃, is a variable resistor which is adjusted so that when the switch is closed momentarily, the ammeter shows zero current flow. (a) Determine R_x in terms of R₁, R₂ and R₃. (b) If a Wheatstone bridge is “balanced” when R₁ = 685 Ω, R₂ = 972Ω and R₃ = 78.6Ω, what is the value of the unknown resistance?

(III) The filament of an incandescent lightbulb has a resistance of 12 Ω at 20°C and 140 Ω when hot. In this temperature range, what is the percentage change in resistance due to thermal expansion, and what is the percentage change in resistance due solely to the change in ρ? Use Eq. 25–5.

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.

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?

Household wiring has sometimes used aluminium instead of copper. What would be the resistance of the same wire if it were made of aluminum?

The cross section of a portion of wire increases uniformly as shown in Fig. 25–38 so it has the shape of a truncated cone. The diameter at one end is a and at the other it is b, and the total length along the axis is ℓ. If the material has resistivity ρ, determine the resistance R between the two ends in terms of a, b, ℓ, and ρ. Assume that the current flows uniformly through each section, and that the taper is small, i.e., ( b -a) ≪ ℓ.

Electricity can be a hazard in hospitals, particularly to patients who are connected to electrodes, such as an ECG. Suppose that the motor of a motorized bed shorts out to the bed frame, and the bed frame’s connection to a ground has broken (or was not there in the first place). If a nurse touches the bed and the patient at the same time, the nurse becomes a conductor and a complete circuit can be made through the patient to ground through the ECG apparatus. This is shown schematically in Fig. 26–79. Calculate the current through the patient.

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

A sequence of potential differences V is applied across a wire ( diameter = 0.32 mm, length = 11cm) and the resulting currents I are measured as follows: Plot I vs. V. Based on this plot, can you conclude that the wire obeys Ohm’s law (i.e., did you obtain a straight line with the expected y-intercept, within the values of the significant figures)? If so, determine the wire’s resistance R.