Electric Circuits Answers

How can I find V_o (in function of V and I) in this circuit?
http://i.imgur.com/W3sEDoJ.png

PS: the answer is supposed to be Vo = 5I +Vs/4

Explain why the present of dielectratic increase the capcitance of the capasitor?

the tiny ball at the end of the thread shows in below figure has a mass of 0.609g and is in horizontal electric field of intensity 700 n/c it is in equilibrium in the position. What are the magnitude and sign of the ball?

: on a thin rod of length L lying along the x axis with one end at the origin (x=0), as in figure there is distributed a charge per unit length is given by lambda so that the total charge on the rod is Q=lambda L.
Find an expression for the electric field at point P(O, y).

a molecule having two atoms has a dipole moment of 6*10^-3 cm. the distance between the atoms is 3.75*10^-11m. When the molecule is placed in an external uniform electrostatic field of magnitude 13n/c, its dipole moment makes an angle of 300 with that field.
-draw the system for these conditions and show the direction of the dipole moment vector explicitly
-calculate the amount of charge generating this dipole moment.
-calculate the magnitude of the torque on the dipole

a quadrupole consists of two dipoles that are close to each other, the effective charge at the origin is -2q and the other charges on the y-axis at y=a and y=-a are are +q each. (1) find the electric field at a point on the x-axis far away so that x>>a. (2) find the electric field on the y-axis far away so tha y>>a

The back table at La Fiesta resturant in Elko is slightly tilted. When Hannah places a tennis ball on the top center of the table and gently lets go the ball rolls slowly to the edge and then drops off. This motion is of course caused by gravity acting on the ball. So there are really two motions that the ball undergoes in this problem. First the ball rolls on the table toward the edge with an acceleration much less than 9.8 m/sec^2 but as the ball falls off it suddenly has an acceleration of 9.8 meters/sec^2. The question is, if the motions of the ball are caused by gravity, why does the ball have an acceleration much less than 9.8 m/sec^2 when rolling across the table top toward the edge? In other words, when it is rolling on the table how come the acceleration is not "g"?

A wire of total resistance R is bent in the form of a regular polygon of n-sides. The ratio of max. and min. resistance it can offer is