If the 0.100-mm diameter tungsten filament in a light bulb is to have a resistance of $0.200\ \Omega$ at $20.0^{\circ} \mathrm{C},$ how long should it be?

(a) Find the size of the smallest detail observable in human tissue with 20.0-MHz ultrasound. (b) Is its effective penetration depth great enough to examine the entire eye (about 3.00 cm is needed)? (c) What is the wavelength of such ultrasound in $0^{\circ} \mathrm{C}$ air?

(a) What resistance would you put in parallel with a $40.0-\Omega$ galvanometer having a $25.0 - \mu \mathrm{A}$ sensitivity to allow it to be used as an ammeter that has a full-scale deflection for $10.0-\mu \mathrm{A}?$ (b) What is unreasonable about this result? (c) Which assumptions are responsible?

What current flows through a 2.54-cm-diameter rod of pure silicon that is 20.0 cm long, when 1.00 $\times$ 10$^3$ V is applied to it? (Such a rod may be used to make nuclearparticle detectors, for example.)

A high-energy proton accelerator produces a proton beam with a radius of $r=0.90 \mathrm{~mm}$. The beam current is $I=9.00 \mu \mathrm{A}$ and is constant. The charge density of the beam is $n=6.00 \times 10^{11}$ protons per cubic meter. $(a)$ What is the current density of the beam? $(b)$ What is the drift velocity of the beam? $(c)$ How much time does it take for $1.00 \times 10^{10}$ protons to be emitted by the accelerator?

A high-energy proton accelerator produces a proton beam with a radius of r = 0.90 mm . The beam current is I = 9.00 $\mu$A and is constant. The charge density of the beam is n = 6.00 $\times$ 10$^{11}$ protons per cubic meter. (a) What is the current density of the beam? (b) What is the drift velocity of the beam? (c) How much time does it take for 1.00 $\times$ 10$^{10}$ protons to be emitted by the accelerator?

The quantity of charge through a conductor is modeled as $Q=4.00 \frac{\mathrm{C}}{\mathrm{s}^4} t^4-1.00 \frac{\mathrm{C}}{\mathrm{s}} t+6.00 \mathrm{mC}$. What is the current at time $t=3.00 \mathrm{~s}$ ?

The quantity of charge through a conductor is modeled as $Q = 4.00 \frac { \mathrm { C } } { \mathrm { s } ^ { 4 } } t ^ { 4 } - 1.00 \frac { \mathrm { C } } { \mathrm { s } } t + 6.00 \mathrm { mC }$. What is the current at time t = 3.00 s?

How many electrons flow through a point in a wire in 3.00 s if there is a constant current of I = 4.00 A?

Show that if there is a positive integer n such that $dA^{n}=\mathbf{0}$, then $\lambda=0$ is the only eigenvalue of A.

Two different electrical devices have the same power consumption, but one is meant to be operated on 120-V AC and the other on 240-V AC. (a) What is the ratio of their resistances? (b) What is the ratio of their currents? (c) Assuming its resistance is unaffected, by what factor will the power increase if a 120 -V AC device is connected to 240-V AC?

Write each decimal as a fraction or mixed number in simplest form. 0.375

Determine whether the statement is true or false. If A is a $2 \times 2$matrix that has two distinct eigenvalues $\lambda_{1}$ and $\lambda_{2}$, then $\operatorname{tr}(A)=\lambda_{1}+\lambda_{2}$.

For the following exercise, use the following table, which shows the height h of the Saturn V rocket for the Apollo 11 mission t seconds after launch.

$$\begin{matrix} \text{Time (seconds)} & \text{Height (meters)}\\ \text{0} & \text{0}\\ \text{1} & \text{2}\\ \text{2} & \text{4}\\ \text{3} & \text{13}\\ \text{4} & \text{25}\\ \text{5} & \text{32}\\ \end{matrix}$$

The best quadratic fit to the data is given by $G(t)=1.429 t^{2}+0.0857 t-0.1429$, where G is the height of the rocket (in meters) and t is the time elapsed since takeoff. From this equation, determine G'(t). Graph G(t) with the given data and, on a separate coordinate plane, graph G'(t).