What is the difference between series and parallel circuits? specify in words and algebraic formula, if possible, the relationships between current, voltage, and resistance in each type of circuit.

Series Circuit.

There is only one path in which electrons can flow in a circuit.

Algebraic Formulas (for n number of components)

I = I1 = I2 = I3 =In

V= V1 + V2 + V3 + - - -  + Vn

Req = R1 + R2 + R3 + - - -  + Rn

Vn = I Rn                

Parallel Circuit.

There is more than one path in which electrons can flow in a circuit.

Algebraic Formulas

I = I1 + I2 + I3 = - - - - - +In

V= V1 = V2 = V3 + - - - - - = Vn  

1/Req = 1/R1 + 1/R2 + 1/R3 + - - - - - + 1/Rn

V = In Rn  

jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west