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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...