# Search results

19. ### Deriving Capacitor Voltage for a Discharging Capacitor

Homework Statement I'm trying to derive the voltage waveform across the capacitor for a discharging capacitor that has been fully charged by a DC power supply ##v_0##, i.e. ##v_c(t=0)=v_0## and then at ##t=0## the switch is flipped and the capacitor starts to discharge. Homework Equations...
20. ### Thevenin's Theorem Problem

Homework Statement Determine the voltage across ##R_3## in the following figure assuming an input voltage ##v_0## of 10V is applied across the open terminals. Let ##R_1=3\Omega##, ##R_2=15\Omega##, ##R_3=10\Omega##, ##R_4=5\Omega## and ##R_5=2\Omega## and Homework Equations The Attempt at...
21. ### Simplifying output for a XOR gate using Boolean Algebra

Homework Statement I'm trying to show that the output of this XOR circuit is ##F=A'B+AB'##, Homework Equations ##(A+B)'=A'\cdot B'## ##(A\cdot B)'=A'+B'## The Attempt at a Solution From the gates the output is ##[(A\cdot B)+(A+B)']'##, using De Morgan's laws this becomes ##[(A\cdot...
22. ### Finding Internal Resistance of a Battery

Homework Statement A real battery can be modeled as an ideal voltage source in series with a resistor. A voltmeter with input resistance of ##1000\Omega## measures the voltage of a 1.5V worn out battery as 0.9V. What is the internal resistance of the battery. Homework Equations ##V=IR## The...
23. ### Calculating Center of Mass in Cylindrical Coordinates

Homework Statement Determine the center of mass in cylindrical coordinates of a cone with constant density ##\rho(\vec{r})##. (The cone is inverted, i.e. it's thinnest point is at ##z=0##.) Homework Equations ##m=\int\int\int_C \rho r \, drdzd\theta## ##\overline{r}=\int\int\int_C r\cdot r\...
24. ### Electron in a Finite Square Well

Homework Statement An electron in a finite square well has 6 distinct energy levels. If the finite square well is 10nm long determine: a) Approximate the possible values for the depth of the finite square well ##V_0##. b) Using a well depth value in the middle of the results obtained from part...
25. ### If ##V(x)## is an even function then the energy eigenfunc...

Homework Statement If ##V(x)## is an even function [i.e. ##V(-x)=V(x)##], then the energy eigenfunctions ##\phi_E(x)## can always be taken to be either even or odd. i.e. show ##\psi_{odd}(x)\equiv\frac{\phi_E(x)-\phi_E(-x)}{2}## and ##\psi_{even}(x)\equiv\frac{\phi_E(x)+\phi_E(-x)}{2}##. The...
26. ### Rope falling through a hole on a frictionless table

Homework Statement A rope with uniform density ##\lambda=\frac{m}{L}## is placed on a frictionless table with an initial length ##y_0## hanging through the hole. Derive a differential equation for the position of the bottom of the rope and then using this solve for the time required for the...
27. ### Number of electrons making it through an NPN transistor

Homework Statement Suppose ##n## electrons attempt to move through an ##NPN## transistor, there's a probability that some of the electrons traversing the ##P## area will recombine and and not make it to the other side. The infinitesimal probability in a region dx is given by...
28. ### Complex Impedance of a voltage source and 2 resistors

Homework Statement A real voltage source can be expressed as an ideal voltage source that is in series with a resistor that represents the inner resistance of the voltage source. This voltage source is a EMF and it is also in series with another resistor. Suppose both the EMF resistor...
29. ### Finding values for an RLC circuit graphically

Homework Statement Determine ##q(t=0)##, ##i(t=0)##, the phase difference ##\phi##, angular frequency ##w## and the time constant ##\tau## from the graph of the capacitor waveform below:(pulse voltage source) For this circuit we have ##q(t)=Ae^{-\frac{t}{2\tau}}\cos(\omega t+\phi)##...
30. ### Potential Difference Across Diode & Resistor

Homework Statement Assume an ideal diode with ##V_t=0.6##v, find the potential differences across the diode V_ab and across the resistor V_bc as the forward bias voltage is varied from 0 to 10v. Hint: equivalent circuits may be useful Embedding the image wasn't working so...