Problem 71
A \(12.0 \mathrm{~V}\) battery with an internal resistance \(R_{\mathrm{j}}=4.00 \Omega\) is attached across an external resistor of resistance \(R\). Find the maximum power that can be delivered to the resistor.
Problem 73
The Stanford Linear Accelerator accelerated a beam consisting of \(2.0 \cdot 10^{14}\) electrons per second through a potential difference of \(2.0 \cdot 10^{10} \mathrm{~V}\) a) Calculate the current in the beam. b) Calculate the power of the beam. c) Calculate the effective ohmic resistance of the accelerator.
Problem 75
Three resistors are connected to a power supply with \(V=110 . \mathrm{V}\) as shown in the figure a) Find the potential drop across \(R_{3}\) b) Find the current in \(R_{1}\). c) Find the rate at which thermal energy is dissipated from \(R_{2}\).
Problem 79
Two conducting wires have identical lengths \(L_{1}=L_{2}=\) \(L=10.0 \mathrm{~km}\) and identical circular cross sections of radius \(r_{1}=r_{2}=r=1.00 \mathrm{~mm} .\) One wire is made of steel (with resistivity \(\rho_{\text {steel }}=40.0 \cdot 10^{-8} \Omega \mathrm{m}\) ); the other is made of copper (with resistivity \(\left.\rho_{\text {copper }}=1.68 \cdot 10^{-8} \Omega \mathrm{m}\right)\) a) Calculate the ratio of the power dissipated by the two wires, \(P_{\text {copper }} / P_{\text {steel }},\) when they are connected in parallel; a potential difference of \(V=100 . \mathrm{V}\) is applied to them. b) Based on this result, how do you explain the fact that conductors for power transmission are made of copper and not steel?
Problem 80
Before bendable tungsten filaments were developed, Thomas Edison used carbon filaments in his light bulbs. Though carbon has a very high melting temperature \(\left(3599^{\circ} \mathrm{C}\right)\) its sublimation rate is high at high temperatures. So carbonfilament bulbs were kept at lower temperatures, thereby rendering them dimmer than later tungsten-based bulbs. A typical carbon-filament bulb requires an average power of \(40 \mathrm{~W}\), when 110 volts is applied across it, and has a filament temperature of \(1800^{\circ} \mathrm{C}\). Carbon, unlike copper, has a negative temperature coefficient of resistivity: \(\alpha=-0.0005^{\circ} \mathrm{C}^{-1}\) Calculate the resistance at room temperature \(\left(20^{\circ} \mathrm{C}\right)\) of this carbon filament.
Problem 81
A material is said to be ohmic if an electric field, \(\vec{E}\), in the material gives rise to current density \(\vec{J}=\sigma \vec{E},\) where the conductivity, \(\sigma\), is a constant independent of \(\vec{E}\) or \(\vec{J}\). (This is the precise form of Ohm's Law.) Suppose in some material an electric field, \(\vec{E}\), produces current density, \(\vec{J},\) not necessarily related by Ohm's Law; that is, the material may or may not be ohmic. a) Calculate the rate of energy dissipation (sometimes called ohmic heating or joule heating) per unit volume in this material, in terms of \(\vec{E}\) and \(\vec{J}\). b) Express the result of part (a) in terms of \(\vec{E}\) alone and \(\vec{J}\) alone, for \(\vec{E}\) and \(\vec{J}\) related via Ohm's Law, that is, in an ohmic material with conductivity \(\sigma\) or resistivity \(\rho .\)
