In Problems 2 10 We Consider A Simple Electrical Circuit With Voltage V Measured In Volts Resistance R Measured I 1 (56.98 KiB) Viewed 20 times
In problems 2 - 10, we consider a simple electrical circuit with voltage V (measured in volts), resistance R (measured in ohms), and current I (measured in amps). These three positive variables are related to one another by “Ohms Law”: V=IR. We may consider this law as written, or treat I as a function of R and V, and write: I = I(R,V) = 2. Evaluate 1(3, 12), and fully describe what this means. = R 3. Show that the limit lim does not exist by evaluating limits along the (RV)-(0,0) positive R-axis and along the line R = V in the RV-plane.
4. Sketch the contour map for the function : 1 = 1(R,V) = x; include at least 4 level curves. R 6 5 4-1 DN 3 2 1 1 2 3 4 5 6 AX -6 -5 -4 -3 - -2 -1 1 -2- -31 -4- -5 -6 5. Compute the partial derivatives these partial derivatives. a1 OR and ;; explain the meaning of the signs of each of av
6. Use Ohms' Law V = IR to simplify completely the “cyclic” expression: ') 3) 7. Verify Clairaut's Theorem: Irv = Ivr
8. Find the equation of the tangent plane to the surface I = I(R,V) = at R=3, V=12. 9. If the resistance is measured as 3 ohms with a possible error of 0.05 ohms, and the voltage is measured as 12 volts with a possible error of 0.2 volts, use differentials to estimate the propagated error in the calculation of the current.
10. Suppose that the voltage is decreasing at the rate of 0.1 volt/sec as the battery wears out, and that the resistance is increasing at the rate of 2 ohms/sec as the wire heats up. Determine the rate at which the current I is changing when R=3, V=12.
Join a community of subject matter experts. Register for FREE to view solutions, replies, and use search function. Request answer by replying!