A battery is connected to three resistors made from the same material in series and have the same lengths but different radii. The drift speed of charge carriers in each resistor has the relationship 4v1 = 16v2 = v3. What is the relationship between the radii?

A uniformly distributed current of 2.0 A is carried by a hollow cylindrical conductor of outer radius b = 2.0 cm  and inner radius a = 1.5 cm. What is the magnitude of the magnetic field due to this current at a location 2.5 mm beneath the outer surface of the conductor?

Two concentric wires, with radii b and 2b lie in the same plane each with current I in opposite directions giving a net magnetic field B at the center of the loops pointing out of the page. If the currents are to remain in opposite directions, what current is required in the outer loop such that the net magnetic field has magnitude B, but points into the page? 

A 12-year-old boy visited his pediatrician complaining of worsening headache, congestion, and pain to his nose and forehead upon touch. His mother said he spiked a fever of 102°F the previous day. He was diagnosed with a sinus infection and given a subcutaneous injection of penicillin. Four days later the patient visited the emergency department with fever; chills; swelling in his hands, feet, ankles, and face; and a urticarial rash covering his abdomen and thighs. The patient was diagnosed with serum sickness and was given anti-inflammatory corticosteroids, after which his symptoms improved rapidly. Questions: Serum sickness involves deposition of immune complexes in local tissues causing inflammation. Describe the process of inflammation. Patients with serum sickness can have an increase in acute phase reactants (APR). List the most important acute phase reactants. What is the most important APR and its mechanism of action? Hint: Question #1

Four identical lightbulbs with the same resistance each are connected to an ideal battery as shown below. Bulb R2 is removed. How does the brightness of the remaining bulbs change? It might help to remember that the brightness of identical bulbs is an observable measure of the power dissipated by the bulbs.  

What is V1 − V2 in the circuit below? The arrows indicate the known values and directions for the current at their placements. The resistor R has unknown resistance.

What is \(\frac{\partial \cos(xyz)}{\partial x}\)?

Passage 2 Which of the following is implied based on the text?

Find the volume of the space beneath the graph of the function \(f(x,y)=\sqrt{1-x^2-y^2}\) over the unit disk.

Compute the gradient of the following function \(f(x,y,z)=xyz\).