# Search results

1. ### Proof of Euler's Theorem

Homework Statement If the divisor P is a prime of the form 4q+1 then the number -1 or P-1 is certainly a residue. Homework Equations The Attempt at a Solution First the book told me to prove that 1 and -1 are the only two remainders that are their own reciprocals modP...
2. ### Output impedance of a Pass Transistor

Homework Statement Calculate the output impedance of the emitter-follower circuit called a pass transistor. Assume that beta=200 **See attached diagram** Homework Equations The Attempt at a Solution Not really sure how this works, I thought it would just be 1k cause that is the...
3. ### Npn transistor with a diode

Homework Statement The absolute max voltage rating for the base-emitter voltage is the lowest of all values. This low value means the B-E junction must be protected from a high reverse voltage. A diode is used for an npn transistor. Explain its function and conditions under which...
4. ### Charging a battery circuit

Homework Statement Make a modification so that the battery is charged by the DC supply at a current of 10mA **See attached diagram** Homework Equations The Attempt at a Solution Well I know that I would put in a resistor in parallel with the diode. However, I don't know how...
5. ### Circuits with Diodes

Homework Statement sketch the output waveforms when a 5Vp sine wave with a frequency of 100 Hz is applied to each of the following circuits **see attached diagrams** Homework Equations The Attempt at a Solution
6. ### Circuit with a zener diode

Homework Statement What would happen if the load resistor was short-circuited. What would happen if the load resister was removed? -see attached diagram- Homework Equations P=Iin^2*R Pz=IzVz =(Iin-Iout)Vz=[((Vin-Vz)/R)-Iout]Vz The Attempt at a Solution I'm not sure about...
7. ### Current from a sine wave signal

Homework Statement Given a sine wave signal (20V PP) connected to a 10 kilo-Ohm resistor. Calculate the current through the resistor in terms of average, rms, and peak currents. What wattage rating should the resistor have? Homework Equations Vrms=(1/Sqrt(2))(Vp) V=IR The Attempt...
8. ### RL to RC circuit

Homework Statement Design a RC circuit so it has the same V vs time characteristics *See attached diagram* Homework Equations The Attempt at a Solution I really have no idea how to approach this, but I do know, RC circuit: Vc(t)=Vb(1-e^-(t/RC)) RL circuit...
9. ### RL to RC circuit

Homework Statement Design an RC circuit that has the same Voltage vs. Time characteristics as the RL circuit shown *See attached Diagram* Homework Equations The Attempt at a Solution Not really sure how to approach this, but all i know is the equations: RC circuit...
10. ### Graph of RC circuit

Homework Statement Sketch a graph of Vout vs time after the switch is closed *See attached diagram* Homework Equations The Attempt at a Solution I am not really sure how to do this, because I don't know if it makes a difference whether or not the resistor is before the...
11. ### Current in multi-battery circuits

Homework Statement Find the current through R2 (see attached figure) Homework Equations The Attempt at a Solution Not really sure if I did this right, would like if someone would double check my work: First I tried Using Kirchhoff equations for a node and I got: I1-I2+I3=0 Next I broke...
12. ### Internal Resistance of a Battery problem

Homework Statement A voltmeter whose resistance is 1000 ohms measures the voltage of a worn out 1.5V battery as .9V. What is the internal Resistance Homework Equations The Attempt at a Solution In order to do this, I Solved for the Equiv Resistance of the circuit (leaving in...
13. ### Current in Open Circuits

Homework Statement Looking at the open circuit demonstrated in figure 2 (see attachment), what is the current through the ammeter? What is the voltage at point p? Homework Equations The Attempt at a Solution I am assuming if it an open circuit, I would think that the current...
14. ### Voltage Divider

Homework Statement How do you measure the output of a voltage divider with real voltmeters that have effective resistances Homework Equations The Attempt at a Solution I know that for an ideal voltmeter (one with infinite resistance), the voltage divider is R2/(R1+R2), but I...
15. ### Diffraction Limited Object Size

Homework Statement What is the diffraction-limited object size (at 25 cm) imposed by the numerical aperture of the eye (if the eye is a diffraction-limited optic)? Use 4mm for the iris diameter and 550 nm for the wavelength. Homework Equations Rayleigh criterion states: for angular...
16. ### Prisms and Images

Homework Statement (2) For the combination of one prism and 2 lenses shown (Fig. 1), find the location and size of the final image when the object, length 1 cm, is located as shown in the figure. [Hint: Treat the prism as a mirror, but you have to take into account the image shift caused by...
17. ### Polarization and Fermat's principle

Homework Statement a) A beam of light in the air strikes the surface of a smooth piece of plastic having an index of refraction of 1.55 at an angle with the normal of 60 degrees. The incident light has equal component E-field amplitudes parallel and perpendicular to the plane of incidence...
18. ### Hyperbolic geometry

Homework Statement How to show that there exists a triangle whose defect is greater than 14 degrees Homework Equations The Attempt at a Solution No idea what to do here.... something about the angle of parallelism
19. ### Proof of Scalene Triangle

Homework Statement Prove that a scalene triangle exists Homework Equations The Attempt at a Solution I really don't know how to approach this proof.... should I do a direct proof or maybe by contradiction? Any help would be great...
20. ### Simple Geometry Proof (Betweenness Axiom)

Homework Statement Given a line l, a point A on l, and a point B not on l. Then every point of the ray AB (except A) lies on the same side of l as B. Homework Equations The Attempt at a Solution I understand why this is true, however I'm having some trouble wording my proof...
21. ### Differentiable functions proof

Homework Statement Consider a function g : (a, b)-->R. Assume that g is differentiable at some point c in (a,b) and that g'(c) is not = 0. Show that there is a delta > 0 so that g(x) is unequal to g(c) for all x in V_delta(c)\{c}intersect(a,b) Homework Equations The Attempt at a...
22. ### Analysis derivative proof

Homework Statement Let f : (a, b)--> R be differentiable on (a,b), and assume that f'(x) unequal 1 for all x in (a,b). Show that there is at most one point c in (a,b) satsifying f(c) = c. Homework Equations The Attempt at a Solution I think that We need to use the mean value...
23. ### Functions and the Intermediate Value theorem

Homework Statement Let f : [0; 1] --> R be continuous on [0, 1], and assume that the range of f is contained in [0; 1]. Prove that there exists an x in [0, 1] satisfying f(x) = x. Homework Equations The Attempt at a Solution Well i am almost positive I need to use the...
24. ### Planar graph induction proof

Homework Statement Let G be a planar graph with n vertices, q edges, and k connected components. If there are r regions in a planar representation of G, prove that: n − q + r = 1 + k Hint: Use induction on k. The base case is Euler’s formula. Homework Equations The Attempt at a...
25. ### Graph theory line graph proof

Homework Statement Let G be a non-empty graph of order n whose vertices have degrees d1, . . . , dn. The line graph of G is defined as follows: the vertices of L(G) are the edges of G, and two vertices of L(G) are adjacent if they share an endpoint in G. Prove that the size of L(G) is...
26. ### Continuous function and limits

Homework Statement Consider a function f : R--> R, and assume that there is a c is in (0, 1) so that |f(x) - f(y)|<= c|x -y| for all x, y in R. (a) Show that f is continuous on R. (b) Given a point y1 in R de fine a sequence by yn+1 = f(yn). Prove that yn is a Cauchy sequence (and...
27. ### Isolated points and continuity

Homework Statement Let f : A --> R be a function, and let c in A be an isolated point of A. Prove that f is continuous at c Homework Equations The Attempt at a Solution I'm kind of confused by this problem.... if c is an isolated point, then the limit doesn't exist. So I can't...
28. ### Limit proof (using delta-epsilon definition)

Homework Statement Let f, g : A \rightarrow R be functions and let c \in R be a limit point of A. Assume that lim(x-> c): f(x) = L and lim(x->c): g(x) = M. Use the epsilon-delta definition to prove: lim(x->c) f(x)g(x)=LM Homework Equations The Attempt at a Solution alright in...
29. ### Compact sets and sup/inf

Homework Statement Show if K contained in R is compact, then supK and inf K both exist and are elements of K. Homework Equations The Attempt at a Solution Ok we proved a theorem stating that if K is compact that means it is bounded and closed. So if K is bounded that means...
30. ### Open and Closed sets

Homework Statement Let E be a nonempty subset of R, and assume that E is both open and closed. Since E is nonempty there is an element a \in E. De note the set Na(E) = {x > 0|(a-x, a+x) \subsetE} (a) Explain why Na(E) is nonempty. (b) Prove that if x \in Na(E) then [a-x, a+x] \subset...